International Congress of Mathematicians: Discrete Mathematics

ICM 2018 - Rio

Discrete Mathematics and Computer Science

Discrete Mathematics and Computer Science

Model Theory and the Philosophy of Mathematical Practice Formalization without Foundationalism John T. Baldwin

Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.

January 2018 247 x 174 mm 362pp 8 b/w illus.

978-1-107-18921-8 Hardback £90.00 / US$120.00 C

Higher Categories and Homotopical Algebra Denis-Charles Cisinski Cambridge Studies in Advanced Mathematics January 2020 978-1-108-47320-0 Hardback TBA / TBA

Lambda Calculus with Types Henk Barendregt Wil Dekkers and Richard Statman

This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification.

Perspectives in Logic

The Homotopy Theory of (∞1)-Categories

Synthetic Differential Topology

Julia E. Bergner

Marta Bunge, Felipe Gago and Ana María San Luis

An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.

London Mathematical Society Student Texts, 90

Represents the state of the art in the new field of synthetic differential topology.

London Mathematical Society Lecture Note Series, 448

June 2013 228 x 152 mm 856pp 52 b/w illus. 300 exercises 978-0-521-76614-2 Hardback £65.00 / US$91.00 C

March 2018 228 x 152 mm 284pp 978-1-107-49902-7 Paperback £29.99 / US$39.99 P

March 2018 228 x 152 mm 232pp 23 b/w illus.

978-1-108-44723-2 Paperback £50.00 / US$80.00 C

The Once and Future Turing

Set Theory

Turing’s Legacy

A First Course Daniel W. Cunningham

Developments from Turing’s Ideas in Logic Edited by Rod Downey

Computing the World Edited by S. Barry Cooper and Andrew Hodges

Original essays by world-leading researchers reveal Alan Turing’s lasting contributions to modern research.

March 2016 247 x 174 mm 395pp 49 colour illus. 4 tables 978-1-107-01083-3 Hardback £19.99 / US$31.99 G

Set theory can be considered a unifying theory for mathematics.

This book covers the fundamentals of the subject.

Cambridge Mathematical Textbooks July 2016 228 x 152 mm 262pp 13 b/w illus.

978-1-107-12032-7 Hardback £40.99 / US$60.99 X

A collection of essays celebrating the influence of Alan Turing’s work in logic, computer science and related areas.

Lecture Notes in Logic, 42 May 2014 228 x 152 mm 539pp 978-1-107-04348-0 Hardback £54.99 / US$76.99 C

20% discount online at www.cambridge.org/ICM2018

Discrete Mathematics and Computer Science

Descriptive Complexity, Canonisation, and Definable Graph Structure Theory

Why Is There Philosophy of Mathematics At All?

Martin Grohe

Hacking explores how mathematics became possible for the human race, and how it ensured our status as the dominant species.

This groundbreaking, yet accessible book explores the interaction between graph theory and computational complexity using methods from finite model theory.

Lecture Notes in Logic, 47

Ian Hacking

January 2014 216 x 138 mm 304pp 978-1-107-65815-8 Paperback £21.99 / US$29.99 G

Dense Sphere Packings

Basic Category Theory

A Blueprint for Formal Proofs Thomas Hales

Tom Leinster

The definitive account of the recent computer solution of the oldest problem in discrete geometry.

London Mathematical Society Lecture Note Series, 400 September 2012 228 x 152 mm 286pp 978-0-521-61770-3 Paperback £47.99 / US$79.99 C

A short introduction ideal for students learning category theory for the first time.

Cambridge Studies in Advanced Mathematics, 143 July 2014 228 x 152 mm 190pp 100 exercises 978-1-107-04424-1 Hardback £41.99 / US$67.00 P

August 2017 228 x 152 mm 554pp 60 b/w illus.

978-1-107-01452-7 Hardback £120.00 / US$155.00 C

Type Theory and Formal Proof

Analysis of Boolean Functions

Categorical Homotopy Theory

The Logic of Infinity

An Introduction Rob Nederpelt and Herman Geuvers

Ryan O’Donnell

Emily Riehl

Barnaby Sheppard

This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.

This categorical perspective on homotopy theory helps consolidate and simplify one’s understanding of derived functors, homotopy limits and colimits, and model categories, among others.

This book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets.

A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.

November 2014 247 x 174 mm 466pp 35 b/w illus. 125 exercises 978-1-107-03650-5 Hardback £54.99 / US$82.00 P

June 2014 228 x 152 mm 444pp 13 b/w illus. 450 exercises 978-1-107-03832-5 Hardback £54.99 / US$82.00 P

New Mathematical Monographs, 24

July 2014 247 x 174 mm 498pp 45 b/w illus.

978-1-107-67866-8 Paperback £29.99 / US$46.99 P

August 2014 228 x 152 mm 372pp 55 exercises 978-1-107-04845-4 Hardback £70.00 / US$99.99 C

20% discount online at www.cambridge.org/ICM2018

Discrete Mathematics and Computer Science

Alan M. Turing Centenary Edition Sara Turing Foreword by Martin Davis and Lyn Irvine Afterword by John Turing

Containing never-beforepublished material, this fascinating account sheds new light on one of the greatest figures of the twentieth century.

November 2014 216 x 140 mm 194pp 7 b/w illus.

978-1-107-52422-4 Paperback £9.99 / US$15.99 G

Structural Proof Theory Sara Negri and Jan von Plato Appendix by Aarne Ranta

A concise introduction to structural proof theory, a branch of logic studying the general structure of logical and mathematical proofs.

July 2008 228 x 152 mm 276pp 978-0-521-06842-0 Paperback £31.99 / US$46.99 C

Proof Analysis A Contribution to Hilbert’s Last Problem Sara Negri and Jan von Plato

Presents a new way of applying the methods of proof theory to axiomatic theories and systems of philosophical logic.

June 2014 244 x 170 mm 278pp 978-1-107-41723-6 Paperback £31.99 / US$46.99 C

Elements of Logical Reasoning Jan von Plato

This book provides an accessible and at the same time scientifically rigorous introduction to the principles of logical reasoning.

January 2014 247 x 174 mm 271pp 978-1-107-61077-4 Paperback £16.99 / US$24.99 P

20% discount online at www.cambridge.org/ICM2018