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Proof Complexity (Encyclopedia of Mathematics and its Applications)

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Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key issue in proof complexity, are of course covered in detail. However, upper bounds are not neglected: this book also explores the relations between bounded arithmetic theories and proof systems and how they can be used to prove upper bounds on lengths of proofs and simulations among proof systems. It goes on to discuss topics that transcend specific proof systems, allowing for deeper understanding of the fundamental problems of the subject.
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Computer Graphics Through OpenGL®: From Theory to Experiments
Computer Graphics Through OpenGL®: From Theory to Experiments

COMPREHENSIVE COVERAGE OF SHADERS AND THE PROGRAMMABLE PIPELINE

From geometric primitives to animation to 3D modeling to lighting, shading and texturing, Computer Graphics Through OpenGL®: From Theory to Experiments is a comprehensive introduction to computer graphics which uses an active...

The Algebra of Happiness: Notes on the Pursuit of Success, Love, and Meaning
The Algebra of Happiness: Notes on the Pursuit of Success, Love, and Meaning
An unconventional book of wisdom and life advice from renowned business school professor and New York Times bestselling author of The Four Scott Galloway.

Scott Galloway teaches brand strategy at NYU's Stern School of Business, but his most popular lectures deal with life strategy, not business. In
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Using R for Data Analysis in Social Sciences
Using R for Data Analysis in Social Sciences
Statistical analysis is common in the social sciences, and among the more popular programs is R. This book provides a foundation for undergraduate and graduate students in the social sciences on how to use R to manage, visualize, and analyze data. The focus is on how to address substantive questions with data analysis and replicate...

Fast Forward Investing: How to Profit from AI, Driverless Vehicles, Gene Editing, Robotics, and Other Technologies Reshaping Our Lives
Fast Forward Investing: How to Profit from AI, Driverless Vehicles, Gene Editing, Robotics, and Other Technologies Reshaping Our Lives

Invest in the future! Everything you need to capitalize on the tech revolution

Our lives are on the verge of being reshaped by advanced technology. Fast Forward Investing provides the knowledge and insight you need to build and maintain your portfolio...

The Second Mountain: The Quest for a Moral Life
The Second Mountain: The Quest for a Moral Life
#1 NEW YORK TIMES BESTSELLER • Everybody tells you to live for a cause larger than yourself, but how exactly do you do it? The author of The Road to Character explores what it takes to lead a meaningful life in a self-centered world.

“Deeply moving, frequently eloquent and
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30-Second Nutrition: The 50 most significant food-related facts, each explained in half a minute
30-Second Nutrition: The 50 most significant food-related facts, each explained in half a minute
If you only have 30 seconds, there is time – using this book – to bone  up on how to eat well. We’re served a daily diet of food facts, fads and often far-fetched claims for what we put on our plates, which makes it difficult to distinguish healthy from harmful. With obesity, heart disease,...
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