Set Theory & Logic

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CounterExamples: From Elementary Calculus to the Beginnings of Analysis

CounterExamples: From Elementary Calculus to the Beginnings of Analysis

Andrei Bourchtein, Ludmila Bourchtein

September 09, 2014

This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages students to think critically and analytically, and helps to...

Set Theoretical Aspects of Real Analysis

Set Theoretical Aspects of Real Analysis

Alexander B. Kharazishvili

August 26, 2014

Set Theoretical Aspects of Real Analysis is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue...

Proof Theory: Sequent Calculi and Related Formalisms

Proof Theory: Sequent Calculi and Related Formalisms

Katalin Bimbo

August 20, 2014

Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide...

Understanding Mathematical Proof

Understanding Mathematical Proof

John Taylor, Rowan Garnier

March 21, 2014

The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs. Understanding Mathematical Proof describes the...

A Functorial Model Theory: Newer Applications to Algebraic Topology, Descriptive Sets, and Computing Categories Topos

A Functorial Model Theory: Newer Applications to Algebraic Topology, Descriptive Sets, and Computing Categories Topos

Cyrus F. Nourani

February 06, 2014

This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a...

Mathematics: A Minimal Introduction

Mathematics: A Minimal Introduction

Alexandru Buium

November 14, 2013

Bridging the gap between procedural mathematics that emphasizes calculations and conceptual mathematics that focuses on ideas, Mathematics: A Minimal Introduction presents an undergraduate-level introduction to pure mathematics and basic concepts of logic. The author builds logic and mathematics...

Mechanical Logic in Three-Dimensional Space

Mechanical Logic in Three-Dimensional Space

Gennaro Auletta

October 24, 2013

The book explores how build a mechanical inferences by making use of arithmetic operations on a string of numbers representing statements. In this way logic is reduced to a branch of the combinatory calculus. It covers the field of traditional logic by showing that any kind of inference can be...

Limits of Computation: An Introduction to the Undecidable and the Intractable

Limits of Computation: An Introduction to the Undecidable and the Intractable

Edna E. Reiter, Clayton Matthew Johnson

October 29, 2012

Limits of Computation: An Introduction to the Undecidable and the Intractable offers a gentle introduction to the theory of computational complexity. It explains the difficulties of computation, addressing problems that have no algorithm at all and problems that cannot be solved efficiently. The...

Handbook of Finite State Based Models and Applications

Handbook of Finite State Based Models and Applications

Jiacun Wang

October 16, 2012

Applicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering. Handbook of Finite State Based Models and Applications provides a...

Elements of Advanced Mathematics, Third Edition

Elements of Advanced Mathematics, Third Edition

Steven G. Krantz

March 19, 2012

For many years, this classroom-tested, best-selling text has guided mathematics students to more advanced studies in topology, abstract algebra, and real analysis. Elements of Advanced Mathematics, Third Edition retains the content and character of previous editions while making the material more...

The Universal Computer: The Road from Leibniz to Turing

The Universal Computer: The Road from Leibniz to Turing

Martin Davis

December 13, 2011

The breathtakingly rapid pace of change in computing makes it easy to overlook the pioneers who began it all. Written by Martin Davis, respected logician and researcher in the theory of computation, The Universal Computer: The Road from Leibniz to Turing explores the fascinating lives, ideas, and...

Goedel's Way: Exploits into an undecidable world

Goedel's Way: Exploits into an undecidable world

Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa

October 14, 2011

Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time...

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