Rather than teach mathematics and the structure of proofs simultaneously, this book first introduces logic as the foundation of proofs and then demonstrates how logic applies to mathematical topics. This method ensures that the reader gains a firm understanding of how logic interacts with mathematics and empowers them to solve more complex problems. Topics include: Propositional Logic; Predicates and Proofs; Set Theory; Mathematical Induction; Number Theory; Relations and Functions; Ring Theory; Topology.

The Structure of Proof: With Logic and Set Theory

Science & Math

Michael O'Leary

Mathematics

PRENTICE/HALL

"Uses a combination of great stories and thoughtful analysis to suggest that we must find a way to change the purpose of our corporations if we are to build a society that works for all of us. 
Rebecca M. Henderson, John & Natty McArthur University Professor at Harvard University\n"Fresh, balanced, highly readable and deeply informed" 
John Pepper, former Chairman and CEO of P&G\n"Thought-provoking and insightful, Accountable offers a pragmatic and original roadmap to transform capitalism into a system that's more inclusive, sustainable, and just." 
Dr. Rajiv J. Shah, President of The Rockefeller Foundation\nCapitalism is failing and the tools we are relying on to fix it - corporate social responsibility, divestment, impact investing, and government control - are only making things worse.\n-Chevron boasts about the $50 million per year it spends on renewable energy whilst it spends 200 times that on oil exploration\n-Goldman Sachs touts its 10,000 Women initiative but its board ranks 358th out of the Fortune 500 for gender diversity and women earn 55% less than men do on average\nBy focusing on corporations rather than people, we've put our faith in empty trends and brand-focused window-dressing. Why should those responsible for our current crisis be trusted to fix it?\nIn Accountable, authors Michael O'Leary and Warren Valdmanis offer a blueprint for everyone to take responsibility for using their economic power as consumers, as investors, as employees, and as voters to trigger a fundamental shift away from an economy that is unethical, unfair, and destructive to our environment and institutions. Their investigation cuts through the tired dogma of current economic thinking to reveal a hopeful truth: if we can make our corporations accountable to a deeper purpose, we can make capitalism both prosperous and good.\nTrenchant and gripping, this is an indispensable guide and call to action for citizens to take control of our economic power and hold corporations to a higher standard.

Accountable

Warren Valdmanis

Penguin Random House UK

Guides readers through the development of geometry and basic proof writing using a historical approach to the topic In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfully equipped with the necessary logic to develop a full understanding of geometric theorems. Following a presentation of the geometry of ancient Egypt, Babylon, and China, the author addresses mathematical philosophy and logic within the context of works by Thales, Plato, and Aristotle. Next, the mathematics of the classical Greeks is discussed, incorporating the teachings of Pythagoras and his followers along with an overview of lower-level geometry using Euclid's Elements. Subsequent chapters explore the work of Archimedes, Viete's revolutionary contributions to algebra, Descartes' merging of algebra and geometry to solve the Pappus problem, and Desargues' development of projective geometry. The author also supplies an excursion into non-Euclidean geometry, including the three hypotheses of Saccheri and Lambert and the near simultaneous discoveries of Lobachevski and Bolyai. Finally, modern geometry is addressed within the study of manifolds and elliptic geometry inspired by Riemann's work, Poncelet's return to projective geometry, and Klein's use of group theory to characterize different geometries. The book promotes the belief that in order to learn how to write proofs, one needs to read finished proofs, studying both their logic and grammar. Each chapter features a concise introduction to the presented topic, and chapter sections conclude with exercises that are designed to reinforce the material and provide readers with ample practice in writing proofs. In addition, the overall presentation of topics in the book is in chronological order, helping readers appreciate the relevance of geometry within the historical development of mathematics. Well organized and clearly written, Revolutions of Geometry is a valuable book for courses on modern geometry and the history of mathematics at the upper-undergraduate level. It is also a valuable reference for educators in the field of mathematics.

Revolutions of Geometry (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

wiley

Based on the premise that in order to write proofs, one needs to read finished proofs as well as study both their logic and grammar, Revolutions in Geometry depicts how to write basic proofs in various fields of geometry. This accessible text for junior and senior undergraduates explains the general development of geometry throughout time, discusses the involvement of its major contributors, and places the proofs into the context of geometry's history to illustrate how crucial proof writing is to the job of a mathematician.

Revolutions of Geometry

Reveals the power and majesty of U.S. airplanes of the World War II and Korean Conflict periods, and describes some of the difficulties inherent in restoring surviving examples to airworthy condition

Warbirds: Classic American Fighters & Bombers

Mike Jerram

Norman Pealing

Military Press

United States Sky Spies Since World War I

Littlehampton Book Services Lt

239 pages of excellent text, filled with fabulous color photos. First Edition.

Superbirds

History

Military

Osprey_Publishing

First edition. A Trade Paperback in pictorial wrappers, illustrated. A Fine copy.

Jet Warbirds

Politics & Social Sciences

Politics & Government

Motorbooks Intl

"More than ever before,&nbsp;this is the book our economy needs."&nbsp;-&nbsp;Dr. Rajiv Shah, president&nbsp;of the Rockefeller Foundation "Unwilling to settle for easy answers or&nbsp;superficial changes, O'Leary and Valdmanis push&nbsp;us all to ask more of our economic system."&nbsp;-&nbsp;Senator Michael F. Bennet This provocative book takes&nbsp;us inside the fight to save&nbsp;capitalism from itself. Corporations are broken, reflecting no purpose deeper than profit. But the tools we are relying on to fix them--corporate social responsibility, divestment, impact investing, and government control--risk making our problems worse. With lively storytelling and careful analysis, O'Leary and Valdmanis cut through the tired dogma of current economic thinking to reveal a hopeful truth: If we can make our corporations accountable to a deeper purpose, we can make capitalism both prosperous and good. What happens when the sustainability-driven CEO of Unilever takes on the efficiency-obsessed Warren Buffett? Does Kellogg's--a company founded to serve a healthy breakfast--have a sacred duty to sell sugary cereal if that's what maximizes profit? For decades, government has tried to curb CEO pay but failed. Why? Can Harvard students force the university to divest from oil and gas? Does it even matter if they do? O'Leary and Valdmanis, two iconoclastic investors, take us on a fast-paced insider's journey that will change the way we look at corporations. Likely to spark controversy among cynics and dreamers alike, this book is essential reading for anyone with a stake in reforming capitalism--which means all of us.

Accountable: The Rise of Citizen Capitalism

Business & Money

Business Culture

HarperCollins B and Blackstone Publishing

See the best price to sell, buy, or rent books by Michael O'Leary. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Michael O'Leary

See the best price to sell, buy, or rent books by Michael O'Leary. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

The Structure of Proof: With Logic and Set Theory

Accountable

Revolutions of Geometry (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

Revolutions of Geometry

Warbirds: Classic American Fighters & Bombers

United States Sky Spies Since World War I

Superbirds

Jet Warbirds

Accountable: The Rise of Citizen Capitalism

Accountable: The Rise of Citizen Capitalism