Mathematical foundations

Papers based on a series of workshops where prominent researchers present exciting developments in set theory to a broad audience.

Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science.

For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true.

There has been a common perception that computational complexity is a theory of "e;bad news"e; because its most typical results assert that various real-world and innocent-looking tasks are infeasible.

Completeness is one of the most important notions in logic and the foundations of mathematics.

This influential book discusses the nature of mathematical discovery, development, methodology and practice, forming Imre Lakatos''s theory of ''proofs and refutations''.

Praise for the First Edition"e;Luck, Logic, and White Lies teaches readers of all backgrounds about the insight mathematical knowledge can bring and is highly recommended reading among avid game players, both to better understand the game itself and to improve one's skills.

This volume is based on the successful 6th China-Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011.

This handbook offers the first comprehensive reference guide to the interdisciplinary field of model-based reasoning.

This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic.

Practical Mathematical Cryptography provides a clear and accessible introduction to practical mathematical cryptography.

A good title should be informative enough to illuminate a potential reader on the content of a book.

This volume contains the invited papers from the 1983 British Combinatorial Conference.

This book presents an intuitive picture-oriented approach to the formative processes technique and to its applications.

This book is about Granular Computing (GC) - an emerging conceptual and of information processing.

This book presents an in-depth and critical reconstruction of Prawitz's epistemic grounding, and discusses it within the broader field of proof-theoretic semantics.

This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets.

This volume gathers selected papers presented at the Fourth Asian Workshop on Philosophical Logic, held in Beijing in October 2018.

This book traces the history of the MIT Department of Mathematics-one of the most important mathematics departments in the world-through candid, in-depth, lively conversations with a select and diverse group of its senior members.

Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s.

This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory.

The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics.

This book constitutes the proceedings of the 25th International Symposium on Practical Aspects of Declarative Languages, PADL 2023, which was held in Boston, MA, USA, in January 2023.

This is a collection of new investigations and discoveries on the theory of opposition (square, hexagon, octagon, polyhedra of opposition) by the best specialists from all over the world.

Except for this preface, this study is completely self-contained.

Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras.

This present volume is the Proceedings of the 14th International Conference on Near- rings and Nearfields held in Hamburg at the Universitiit der Bundeswehr Hamburg, from July 30 to August 06, 1995.

This vividly illustrated history of the International Congress of Mathematicians- a meeting of mathematicians from around the world held roughly every four years- acts as a visual history of the 25 congresses held between 1897 and 2006, as well as a story of changes in the culture of mathematics over the past century.

From the editors of the popular Making Mathematics with Needlework, this book presents projects that highlight the relationship between types of needlework and mathematics.

The power and properties of numbers, from basic addition and sums of squares to cutting-edge theoryWe use addition on a daily basis-yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity?

Exploring Geometry, Second Edition promotes student engagement with the beautiful ideas of geometry.

A two-volume advanced text for graduate students.

This textbook offers an introduction to the Eclipse system and a guide to problem-solving for students and practitioners alike.

Model theory is the meta-mathematical study of the concept of mathematical truth.

Artificial Intelligence has already pervaded our lives in so many subtle ways, but how will humans react to the creation of a completely sentient super computer: a hyper-intelligent brain without a body who is as omniscient and omnipresent as the internet itself?

Was Sie schon immer über die Kunst, mathematische Texte zu formulieren, wissen wollten, aber nie zu fragen wagten: Was bedeutet "trivial", "wohldefiniert", "Korollar", "eindeutig", "o.

This book discusses how to design "e;good"e; geometric puzzles: two-dimensional dissection puzzles, polyhedral dissections, and burrs.

This book contains Volume 7 of the Journal of Graph Algorithms and Applications (JGAA).

This book is a collection of creative pieces-poems, short stories, essays, play excerpts-that give shape to mathematical and scientific content.

The Magic Theorem: a Greatly-Expanded, Much-Abridged Edition of The Symmetries of Things presents a wonder- fully unique re-imagining of the classic book, The Symmetries of Things.

This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions.

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice.