Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights key arguments. There are several hundred exercises, providing a wealth of both computational and theoretical practice, as well as appendices summarizing the necessary background in algebra.Now in a newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will continue to provide lecturers and their students with an invaluable resource and a compelling gateway to a beautiful subject.From the reviews: A thoroughly delightful introduction to algebraic number theory Ezra Brown in the Mathematical Reviews An excellent basis for an introductory graduate course in algebraic number theory Harold Edwards in the Bulletin of the American Mathematical Society Read more

A rich, narrative explanation of the mathematics that has brought us machine learning and the ongoing explosion of artificial intelligence Machine learning systems are making life-altering decisions for us: approving mortgage loans, determining whether a tumour is cancerous, or deciding whether someone gets bail. They now influence developments and discoveries in chemistry, biology, and physics the study of genomes, extra-solar planets, even the intricacies of quantum systems. And all this before large language models such as ChatGPT came on the scene. We are living through a revolution in machine learning-powered AI that shows no signs of slowing down. This technology is based on relatively simple mathematical ideas, some of which go back centuries, including linear algebra and calculus, the stuff of seventeenth- and eighteenth-century mathematics. It took the birth and advancement of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we s

I found this book amazing. I read it through quickly because it was so interesting, then turned around and read much of it again. Daniel Kahneman, winner of the Nobel Prize in Economics and bestselling author of Thinking Fast Slow I've been recommending A Brief History of Intelligence to everyone I know. A truly novel, beautifully crafted thesis on what intelligence is and how it has developed since the dawn of life itself." Angela Duckworth, bestselling author of Grit Equal parts Sapiens, Behave, and Superintelligence, but wholly original in scope, A Brief History of Intelligence offers a paradigm shift for how we understand neuroscience and AI. Artificial intelligence entrepreneur Max Bennett chronicles the five breakthroughs in the evolution of human intelligence and reveals what brains of the past can tell us about the AI of tomorrow. In the last decade, capabilities of artificial intelligence that had long been the realm of science fiction have, for the first time, become our reality. AI is n