Thinking about Logic: Classic Essays

Thinking about Logic: Classic Essays

Fifteen classic essays in the philosophy of logic, providing essential grounding in formal logic as a system of thought and highlighting vital connections to other areas of philosophical study.;Intro — Contents — Preface — Part I — Part II — Part III — Part IV — Part V — About the Contributors — Source Credits. Fifteen classic essays in the philosophy of logic, providing essential grounding in formal logic as a system of thought and highlighting vital connections to other areas of philosophical study. …

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Solving Problems in Mathematical Analysis, Part I: Sets, Functions, Limits, Derivatives, Integrals, Sequences and Series (Problem Books in Mathematics)

Solving Problems in Mathematical Analysis, Part I: Sets, Functions, Limits, Derivatives, Integrals, Sequences and Series (Problem Books in Mathematics)

This textbook offers an extensive list of completely solved problems in mathematical analysis. This first of three volumes covers sets, functions, limits, derivatives, integrals, sequences and series, to name a few. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis.Based on the authors years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be …

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Fundamentals of Contemporary Set Theory (Universitext)

Fundamentals of Contemporary Set Theory (Universitext)

Fundamentals of Contemporary Set Theory (Ref:mx.us.ml) This book provides an account of those parts of contemporary set theory of direct relevance to other areas of pure mathematics. The intended reader is either an advanced-level mathematics undergraduate, a beginning graduate student in mathematics, or an accomplished mathematician who desires or needs some familiarity with modern set theory. The book is written in a fairly easy-going style, with minimal formalism. In Chapter 1, the basic principles of set theory are developed in a ‘naive’ manner. Here …

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Self-Reference and Modal Logic (Universitext)

Self-Reference and Modal Logic (Universitext)

It is Sunday, the 7th of September 1930. The place is Konigsberg and the occasion is a small conference on the foundations of mathematics. Arend Heyting, the foremost disciple of L. E. J. Brouwer, has spoken on intuitionism; Rudolf Carnap of the Vienna Circle has expounded on logicism; Johann (formerly Janos and in a few years to be Johnny) von Neumann has explained Hilbert’s proof theory– the so-called formalism; and Hans Hahn has just propounded his own empiricist views of mathematics. The floor is …

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Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach (Encyclopedia of Mathematics and its Applications)

Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach (Encyclopedia of Mathematics and its Applications)

The study of graph structure has advanced with great strides. This book unifies and synthesizes research over the last 25 years, detailing both theory and application. It will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory. The study of graph structure has advanced significantly in recent years: finite graphs can now be described algebraically, enabling them to be constructed out of more basic elements. One can obtain algebraic characterizations of tree-width and …

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Category theory in context

Category theory in context

┬áCategory theory has provided the foundations for many of the twentieth century’s greatest advances in pure mathematics. This concise, original text for a one-semester course on the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, and other topics. Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking …

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Category theory in context

Category theory in context

┬áCategory theory has provided the foundations for many of the twentieth century’s greatest advances in pure mathematics. This concise, original text for a one-semester course on the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, and other topics. Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking …

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Higher Operads, Higher Categories (London Mathematical Society Lecture Note Series)

Higher Operads, Higher Categories (London Mathematical Society Lecture Note Series)

Category theory has experienced a resurgence in popularity recently because of new links with topology and mathematical physics. This book provides a clearly written account of higher order category theory and presents operads and multicategories as a natural language for its study. Tom Leinster has included necessary background material and applications as well as appendices containing some of the more technical proofs that might have disrupted the flow of the text. Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and …

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Higher Operads, Higher Categories (London Mathematical Society Lecture Note Series)

Higher Operads, Higher Categories (London Mathematical Society Lecture Note Series)

Category theory has experienced a resurgence in popularity recently because of new links with topology and mathematical physics. This book provides a clearly written account of higher order category theory and presents operads and multicategories as a natural language for its study. Tom Leinster has included necessary background material and applications as well as appendices containing some of the more technical proofs that might have disrupted the flow of the text. Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and …

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