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| Author | : Hermann Weyl |
| Publisher | : Courier Corporation |
| Total Pages | : 208 |
| Release | : 2013-09-26 |
| Genre | : Mathematics |
| ISBN | : 0486266931 |
Original anthology features less-technical essays discussing logic, topology, abstract algebra, relativity theory, and the works of David Hilbert. Most have been long unavailable or previously unpublished in book form. 2012 edition.
| Author | : Rudy Rucker |
| Publisher | : Princeton University Press |
| Total Pages | : |
| Release | : 2019-07-23 |
| Genre | : Mathematics |
| ISBN | : 0691191255 |
A dynamic exploration of infinity In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the “Mindscape,” where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Using cartoons, puzzles, and quotations to enliven his text, Rucker acquaints us with staggeringly advanced levels of infinity, delves into the depths beneath daily awareness, and explains Kurt Gödel’s belief in the possibility of robot consciousness. In the realm of infinity, mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise, we gain profound insights into the human mind, its powers, and its limitations. This Princeton Science Library edition includes a new preface by the author.
| Author | : Hermann Weyl |
| Publisher | : Courier Corporation |
| Total Pages | : 258 |
| Release | : 2012-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486489035 |
This original anthology collects 10 of Weyl's less-technical writings that address the broader scope and implications of mathematics. Most have been long unavailable or not previously published in book form. Subjects include logic, topology, abstract algebra, relativity theory, and reflections on the work of Weyl's mentor, David Hilbert. 2012 edition.
| Author | : Rudy Rucker |
| Publisher | : Courier Corporation |
| Total Pages | : 337 |
| Release | : 2013-11-21 |
| Genre | : Computers |
| ISBN | : 0486492281 |
Originally published: Boston: Houghton Mifflin, 1987.
| Author | : Richard Evan Schwartz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 178 |
| Release | : 2018 |
| Genre | : Infinite |
| ISBN | : 1470447363 |
Mathematics professor from Brown University uses colorful illustrations and cartoons to display the concepts of infinity and large numbers.
| Author | : N.Ya. Vilenkin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 151 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1461208378 |
The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of infinite sets and the subsequent discovery, soon after, of paradoxes in this theory. At the time, many scientists ignored the paradoxes and used set theory extensively in their work, while others subjected set-theoretic methods in mathematics to harsh criticism. The debate intensified when a group of French mathematicians, who wrote under the pseudonym of Nicolas Bourbaki, tried to erect the whole edifice of mathematics on the single notion of a set. Some mathematicians greeted this attempt enthusiastically while others regarded it as an unnecessary formalization, an attempt to tear mathematics away from life-giving practical applications that sustain it. These differences notwithstanding, Bourbaki has had a significant influence on the evolution of mathematics in the twentieth century. In this book we try to tell the reader how the idea of the infinite arose and developed in physics and in mathematics, how the theory of infinite sets was constructed, what paradoxes it has led to, what significant efforts have been made to eliminate the resulting contradictions, and what routes scientists are trying to find that would provide a way out of the many difficulties.
| Author | : Alain Badiou |
| Publisher | : A&C Black |
| Total Pages | : 561 |
| Release | : 2007-07-15 |
| Genre | : Philosophy |
| ISBN | : 082649529X |
A translation of one of the single most important works of recent French philosophy, Badiou's magnum opus, and a must-have for his growing following and anyone interested in contemporary Continental thought.
| Author | : Eugenia Cheng |
| Publisher | : Profile Books |
| Total Pages | : 204 |
| Release | : 2017-03-09 |
| Genre | : Mathematics |
| ISBN | : 1782830812 |
SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.
| Author | : Ivan Penkov |
| Publisher | : Springer Nature |
| Total Pages | : 245 |
| Release | : 2022-01-05 |
| Genre | : Mathematics |
| ISBN | : 3030896609 |
Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
| Author | : Edward Frenkel |
| Publisher | : Basic Books |
| Total Pages | : 314 |
| Release | : 2013-10-01 |
| Genre | : Mathematics |
| ISBN | : 0465069959 |
An awesome, globe-spanning, and New York Times bestselling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.
