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-in the area of cryptography, where the security of your credit card, and indeed of the nation's defense, depends on a result concerning prime numbers that dates back to the eighteenth century. Recent years have witnessed other spectacular developments, such as Andrew Wiles's proof of 'Fermat's last theorem' (unproved for over 250 years) and some exciting work on prime numbers. In this Very Short Introduction Robin Wilson introduces the main areas of classical number theory, both ancient and modern. Drawing on the work of many of the greatest mathematicians of the past, such as Euclid, Fermat, Euler, and Gauss, he situates some of the most interesting and creative problems in the area in their historical context.
Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing the Universe shows you:
● Why cans, pizza, and manhole covers are round.
● Why one and two weren't considered numbers by the ancient Greeks.
● Why squares show up so often in goddess art and board games.
● What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies.
● How the human body shares the design of a bean plant and the solar system.
● And much more.
How is a subway map different from other maps? What makes a knot knotted? What makes the Möbius strip one-sided? These are questions of topology, the mathematical study of properties preserved by twisting or stretching objects. In the 20th century topology became as broad and fundamental as algebra and geometry, with important implications for science, especially physics.
In this Very Short Introduction, Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field.
'Einer der größten abendländischen Denker überhaupt, ein Denker vom Rang und der Tiefe eines Leibniz.' So nannte der Philosoph Heinrich Scholz den 1848 in Wismar geborenen und 1925 in Bad Kleinen verstorbenen Mathematiker, Logiker und Philosophen Gottlob Frege. Mittlerweile legendär ist Gottlob Freges Unterscheidung von Sinn und Bedeutung am Beispiel des Planeten Venus: 'Es würde die Bedeutung von Abendstern und Morgenstern dieselbe sein, aber nicht der Sinn.' Das vorliegende Hörbuch vereint vier wichtige Schriften Gottlob Freges:
'Über Sinn und Bedeutung' - Hier differenziert und entfaltet Frege die zentralen Begriffe Sinn, Bedeutung, Gedanke und Vorstellung.
'Über Begriff und Gegenstand' - Eine Ergänzung und Fortführung zu 'Über Sinn und Bedeutung', hier werden entsprechend dem Titel die Begriffe Begriff und Gegenstand entfaltet.
'Über die wissenschaftliche Berechtigung einer Begriffsschrift' - Hier erläutert Frege die Notwendigkeit der Einführung einer Kunstsprache für die Wissenschaften, seiner Begriffsschrift.
'Was ist eine Funktion?' - Frege nähert sich hier dem für die Mathematik so wichtigen Begriff der Funktion.
Gottlob Frege hat sowohl für die heutige Philosophie als auch für die moderne Logik die entscheidenden Grundlagen gelegt. Nebenbei bemerkt: Ohne seine Arbeit wären Programmiersprachen heute kaum denkbar. Dieses Hörbuch ist ein Muss.
An inclusive vision of mathematics-its beauty, its humanity, and its power to build virtues that help us all flourish
For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas.
In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires-such as for play, beauty, freedom, justice, and love-and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can-and must-be open to all.
Randomness is a concept used (and less formally) in mathematics to imply that there is no way to accurately predict an event (to know what will happen before it takes place) or to sense a trend. Anything that is randomly selected for no conscious purpose can be assumed to be simply by chance factor. An illustration of an occurrence random event is a financial windfall, a lottery win. A computer can generate lists of seemingly random numbers. It is difficult for humans to do the same, since the brain functions in patterns.
If someone is asked to keep repeating heads or tails at random, a considerate human observer or a reasonably programmed computer may eventually tell which one the person is likely to say next because the computer recognizes the patterns. The user can click on Random Page on a website such as English Wikipedia to get a random article. The odds of being on anyone's webpage are the same as on every other webpage.
Born and raised in a small town in Prussia, Friedrich Wilhelm Nietzsche (1844-1900) began his career in philology (the study of language), and served as a professor at the University of Basel. In 1879, he was forced to leave due to health issues, which afflicted him throughout his life. Supported by his university pension and aided by friends, he spent the next decade as an independent author, writing the books for which he would become famous, including Thus Spake Zarathustra, Beyond Good and Evil, and On the Genealogy of Morals. In 1889, at the age of 44, Nietzsche had a mental breakdown from which he never recovered, dying in 1900. Yet in just ten years, he produced a body of work that would mark him as one of the most influential philosophers of all time.
In Simply Nietzsche, Professor Peter Kail traces the development of Nietzsche’s thought through the various phases of his life. Emphasizing the philosopher’s critique of modern morality and his revolutionary conception of the self, he also discusses key motifs of Nietzsche’s thought, such as the death of God, the will to power, and the eternal recurrence.
Even those who have never read Nietzsche or are unsure of why he’s important have heard his name. With Prof. Kail as a guide, Simply Nietzsche provides an unparalleled and accessible introduction to the life and ideas of this most remarkable thinker.
Banish math anxiety and give students of all ages a clear roadmap to success
Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler-Stanford researcher, professor of math education, and expert on math learning-has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students.
There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all.
The solution to your troubles is contained in the wisdom of the ancients.
Stoicism is a philosophy that was started in Ancient Greece, but this two-thousand-year-old worldview is enjoying a modern rebirth. All across the globe, people are coming to appreciate the timeless wisdom of Stoicism.
You don’t have to suffer. You may not be able to control the path your life will take, but Stoicism teaches that you can control the way you see life. By shifting your way of thinking you can eliminate unnecessary suffering, reshape your thought patterns, and achieve that sense of calm you’ve always wanted.
In this book, you will find all of the information you need to understand Stoic thought and put it into action in your life.Gain insight into the emotions that can keep you from living the life that you want to lead. Find out how to master your heart by feeding positive emotions while starving the negative.Learn a strategy for success that has helped some of history’s greatest heroes to triumph in the face of tragedy. When you learn to see obstacles as opportunities you can rise to the top while others fall behind.Find out how to prepare yourself for any challenge life may hand you. Don’t wait for tragedy to strike before you learn how to handle it. Start building the skills that will allow you to weather any storm.You don’t have to live a life ruled by stress and worry. No matter who you are, you can learn how to master your own mind and retake control of your life. The power to change is inside of you, the ancient secrets of Stoicism will show you how to unlock your full potential.
Adrián Paenza, galardonado con el Premio Leelavati al mejor divulgador del mundo en matemática, narra los problemas más curiosos sobre matemática recreativa.
Desde la historia Sofia Kovalevskaya, una matemática rusa que luchó contra el machismo de su época e hizo contribuciones invalorables para la ciencia, hasta números tan grandes que son una locura, los 121 millones de kilómetros que debe cubrir Santa Claus para entregar los regalos todos los años, qué pasa cuando un docente se equivoca, cómo evitar ser un analfabeto del siglo XXI, la excepción que confirma la regla, qué condiciones hay que reunir para ser un niño prodigio, ¿podremos volver a ser anónimos alguna vez?, cien personas con sombrero y muchos otros problemas para escuchar, deducir y quedarnos pensando hasta encontrar una, o más soluciones.
From the author of 'The Music of the Primes' and 'Finding Moonshine' comes a short, lively book on five mathematical problems that just refuse be solved - and on how many everyday problems can be solved by maths.
Every time we download a song from Itunes, take a flight across the Atlantic or talk on our mobile phones, we are relying on great mathematical inventions. Maths may fail to provide answers to various of its own problems, but it can provide answers to problems that don't seem to be its own - how prime numbers are the key to Real Madrid's success, to secrets on the Internet and to the survival of insects in the forests of North America.
In 'The Number Mysteries', Marcus du Sautoy explains how to fake a Jackson Pollock; how to work out whether or not the universe has a hole in the middle of it; how to make the world's roundest football. He shows us how to see shapes in four dimensions - and how maths makes you a better gambler. He tells us about the quest to predict the future - from the flight of asteroids to an impending storm, from bending a ball like Beckham to predicting population growth.
It's a book to dip in to; a book to challenge and puzzle - and a book that gives us answers.
