Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos.This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, ...

A mathematical formalization of Chomsky’s theory of Merge in generative linguistics.The Minimalist Program advanced by Noam Chomsky thirty years ago, focusing on the biological nature of human language, has played a central role in our modern understanding of syntax. One key to this program is the notion that the hierarchical structure of human language syntax consists of a single operation Merge. For the first time, Mathematical Structure of Syntactic Merge

Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story.In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lo...

Modified gravity models play an important role in contemporary theoretical cosmology. The present book proposes a novel approach to the topic based on techniques from noncommutative geometry, especially the spectral action functional as a gravity model. The book discusses applications to early universe models and slow-roll inflation models, to the problem of cosmic topology, to non-isotropic cosmologies like mixmaster universes and Bianchi IX gravitational instantons, and to multifractal s...

This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. One of the main questions in the field is understanding when the residues of Feynman integrals in perturbative quantum field theory evaluate to periods of mixed Tate motives. The question originates from the occurrence of multiple zeta values i...

Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world.Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ...

MULTIPLY your chances of understanding DISCRETE MATHEMATICSIf you're interested in learning the fundamentals of discrete mathematics but can't seem to get your brain to function, then here's your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts.Written by award-winning math professor Steven Krantz, Discrete Mathematics Demystified explains this challenging topic in an effective and e...

Despite claiming unbelief in God or any higher power that may have designed or created the world and all that is in it, modern scientists often write and speak of chance as some kind of being or force that can cause things to happen. In one breath they push the evolution agenda and in the next they say that creatures were "designed" with specific traits. In this classic book, R. C. Sproul and Keith Mathison call the scientific world to employ logic and clarity in their di...

Tough Test Questions? Missed Lectures? Not Rnough Time?Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test ...

"A gripping guide to the modern taming of the infinite."—The New York Times. With a new introduction by Neal Stephenson.Is infinity a valid mathematical property or a meaningless abstraction? David Foster Wallace brings his intellectual ambition and characteristic bravura style to the story of how mathematicians have struggled to understand the infinite, from the ancient Greeks to the nineteenth-century mathematical genius Georg Cantor's counterintuitive discovery that the...

Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside The Open Society and Its Enemies as one of Popper's most enduring books and contains insights and arguments that demand t...

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the a...