This book is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which readers construct their own understanding. However, while readers are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers "proof sketches" and helpful technique tips to help readers as they develop their proof writing skills. This book is most successful in a small, seminar style class. Logic, Sets, Induction, Relations, Functions, Elementary Number Theory, Cardinality, The Real Numbers For all readers interested in abstract mathematics.
Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
Popular math at its most entertaining and enlightening. "Zero is really something"-Washington Post A New York Times Notable Book. The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything. In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics. Here are the legendary thinkers—from Pythagoras to Newton to Heisenberg, from the Kabalists to today's astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.
“Net Zero” has been an effective rallying cry for the green building movement, signaling a goal of having every building generate at least as much energy as it uses. Enormous strides have been made in improving the performance of every type of new building, and even more importantly, renovating the vast and energy-inefficient collection of existing buildings in every country. If we can get every building to net-zero energy use in the next few decades, it will be a huge success, but it will not be enough. In Build Beyond Zero, carbon pioneers Bruce King and Chris Magwood re-envision buildings as one of our most practical and affordable climate solutions instead of leading drivers of climate change. They provide a snapshot of a beginning and map towards a carbon-smart built environment that acts as a CO2 filter. Professional engineers, designers, and developers are invited to imagine the very real potential for our built environment to be a site of net carbon storage, a massive drawdown pool that could help to heal our climate. The authors, with the help of other industry experts, show the importance of examining what components of an efficient building (from windows to solar photovoltaics) are made with, and how the supply chains deliver all those products and materials to a jobsite. Build Beyond Zero looks at the good and the bad of how we track carbon (Life Cycle Assessment), then takes a deep dive into materials (with a focus on steel and concrete) and biological architecture, and wraps up with education, policy and governance, circular economy, and where we go in the next three decades. In Build Beyond Zero, King and Magwood show how buildings are culprits but stand poised to act as climate healers. They offer an exciting vision of climate-friendly architecture, along with practical advice for professionals working to address the carbon footprint of our built environment.
#1 NEW YORK TIMES BEST SELLER • In this urgent, authoritative book, Bill Gates sets out a wide-ranging, practical—and accessible—plan for how the world can get to zero greenhouse gas emissions in time to avoid a climate catastrophe. Bill Gates has spent a decade investigating the causes and effects of climate change. With the help of experts in the fields of physics, chemistry, biology, engineering, political science, and finance, he has focused on what must be done in order to stop the planet's slide to certain environmental disaster. In this book, he not only explains why we need to work toward net-zero emissions of greenhouse gases, but also details what we need to do to achieve this profoundly important goal. He gives us a clear-eyed description of the challenges we face. Drawing on his understanding of innovation and what it takes to get new ideas into the market, he describes the areas in which technology is already helping to reduce emissions, where and how the current technology can be made to function more effectively, where breakthrough technologies are needed, and who is working on these essential innovations. Finally, he lays out a concrete, practical plan for achieving the goal of zero emissions—suggesting not only policies that governments should adopt, but what we as individuals can do to keep our government, our employers, and ourselves accountable in this crucial enterprise. As Bill Gates makes clear, achieving zero emissions will not be simple or easy to do, but if we follow the plan he sets out here, it is a goal firmly within our reach.
This book describes and explains the fundamental changes that are now taking place in the most traditional areas of humanities theory and method, scholarship and education. The changes flow from the re-examination of the very foundations of the humanities - its theories of textuality and communication - that are being forced by developments in information technology. A threshold was crossed during the last decade of the twentieth century with the emergence of the World Wide Web, which has (1) globalized access to computerized resources and information, and (2) made interface and computer graphics paramount concerns for work in digital culture. While these changes are well known, their consequences are not well understood, despite so much discussion by digital enthusiasts and digital doomsters alike. In reconsidering these matters, Radiant Textuality introduces some remarkable new proposals for integrating computerized tools into the central interpretative and critical activities of traditional humanities disciplines, and of literary studies in particular.
The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it says (only) that it is false. How, then, should we classify Liar sentences? Are they true or false? A natural suggestion would be that Liars are neither true nor false; that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another. JC Beall presents fourteen new essays and an extensive introduction, which examine the nature of the Liar paradox and its resistance to any attempt to solve it. Written by some of the world's leading experts in the field, the papers in this volume will be an important resource for those working in truth studies, philosophical logic, and philosophy of language, as well as those with an interest in formal semantics and metaphysics.
Mangla Bhoot, a merchant navy captain, has been awarded two chances in life. Not afraid of backing down, he grabs them both. But does he find ultimate happiness? Oh no, Captain! gives us an intimate portrayal of an otherwise often misunderstood, often overlooked section of society.
Bennett Galloway never thought his passion for science and physics would take him to distances that no one would ever travel. He had everything in his life – a beautiful girl, wealth and all the goods to achieve his dream. His dreams were to explore the corners of the universe and to travel in time. The man had made significant strides, and the journey was relentless toward reaching his goal. However, he never thought his past would be a reason for him to fail even though he moved on from it. It was a mistake he had committed, and that had started to haunt him. He wished he could change his past and the consequences of the future, but he knew that the reality was very adamant.
A NEW YORK TIMES NOTABLE BOOK The Babylonians invented it, the Greeks banned it, the Hindus worshipped it, and the Christian Church used it to fend off heretics. Today it's a timebomb ticking in the heart of astrophysics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything. Within the concept of zero lies a philosophical and scientific history of humanity. Charles Seife's elegant and witty account takes us from Aristotle to superstring theory by way of Egyptian geometry, Kabbalism, Einstein, the Chandrasekhar limit and Stephen Hawking. Covering centuries of thought, it is a concise tour of a world of ideas, bound up in the simple notion of nothing.
