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"Trying to understand a system with multiple interacting components - the weather, for example, or the human body, or the stock market - means dealing with two factors: chaos and complexity. If we don't understand these two essential subjects, we can't understand the real world"--Back cover.

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Introducing the Collins Modern Classics, a series featuring some of the most significant books of recent times, books that shed light on the human experience classics which will endure for generations to come.

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To help readers become better at solving real-world problems, this enlightening, entertaining, and inspiring book teaches simple, effective thinking techniques. The goal is not to quickly solve each challenge but to come up with as many different ways of thinking about it as possible.

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A fascinating exploration of a surprising advantage that humans have over our incoming robot masters: we're actually good at maths.

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Alan Turing's 1938 Princeton PhD thesis, "Systems of Logic Based on Ordinals," which includes his notion of an oracle machine, has had a lasting influence on computer science and mathematics. This title presents the typescript of the thesis along with essays.

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Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories.

(Hardback)

In this book, the author introduces classical logic alongside constructive, relevant, comparative, and other nonclassical logics. It begins with brief introductions to informal set theory and general topology, and avoids advanced algebra; thus it is self-contained and suitable for readers with little background in mathematics.

(Hardback)

Relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. This book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings.

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The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems. In this book, Kurt Godel sets forth his proof for this problem.

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One of the greatest revolutions in mathematics occurred when Georg Cantor promulgated his theory of transfinite sets. His religious beliefs led him to expect paradoxes in any concept of the infinite. This work shows that these played an integral part in his understanding and defense of set theory.

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Explains how scientists who study complexity are convinced that certain constant processes are at work in all kinds of unrelated complex systems.

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Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church's contributions to number theory and theories of algorithms and computability laid the theoretical foundations of computer science. This book is a basic source for understanding formal logic.

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A whimsical journey that shows children how the same number can be both big and small.

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This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton Legacy

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