Mathematical foundations

Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications.

Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.

Readings in Fuzzy Sets for Intelligent Systems is a collection of readings that explore the main facets of fuzzy sets and possibility theory and their use in intelligent systems.

Written by two well-known scholars in the field, Combinatorial Reasoning: An Introduction to the Art of Counting presents a clear and comprehensive introduction to the concepts and methodology of beginning combinatorics.

The present collection of papers derives from a philosophy conference organised in the Sicilian town of M ussomeli in September 1991.

This adaptation of an earlier work by the authors is a graduate text and professional reference on the fundamentals of graph theory.

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

Longlisted for the BSHS Hughes Prize 2021A New Year's Present from a Mathematician is an exciting book dedicated to two questions: What is it that mathematicians do?

AN INDISPENSABLE RESOURCE FOR ALL THOSE WHO DESIGN AND IMPLEMENT TYPE-1 AND TYPE-2 FUZZY NEURAL NETWORKS IN REAL TIME SYSTEMSDelve into the type-2 fuzzy logic systems and become engrossed in the parameter update algorithms for type-1 and type-2 fuzzy neural networks and their stability analysis with this book!

At the close of the nineteenth century, we stood on the threshold of one of the greatest periods of science, in which the entire world and understanding of science would be shaken to the core and greatly modified.

Problems in decision making and in other areas such as pattern recogni- tion, control, structural engineering etc.

Algebra & Geometry: An Introduction to University Mathematics, Second Edition provides a bridge between high school and undergraduate mathematics courses on algebra and geometry.

The bulk of this volume consists of invited addresses presented at the Colloquium.

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This textbook introduces enumerative combinatorics through the framework of formal languages and bijections.

This book is the first of a series of technical reports of a key research project of the Real-World Computing Program supported by the MITI of Japan.

Gerhard Gentzen has been described as logic's lost genius, whom Godel called a better logician than himself.

The book is a concise, self-contained and fully updated introduction to automata theory - a fundamental topic of computer sciences and engineering.

Finite Fields are fundamental structures of Discrete Mathematics.

This unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics.

When I first participated in exploring theories of nonmonotonic reasoning in the late 1970s, I had no idea of the wealth of conceptual and mathematical results that would emerge from those halting first steps.

With exercises and projects, Exploring Mathematics supports an active approach to the transition to upper-level theoretical math courses.

Now updated!

Frege is widely regarded as having set much of the agenda of contemporary analytic philosophy.

The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present.

This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic and mathematics, by the best specialists from all over the world.

This book discusses the evolution of security and privacy issues and brings related technological tools, techniques, and solutions into one single source.

Consider this: Robots will one day be able to write poetry and prose so touching that it will make men weep; compose dozens or even hundreds of symphonies that will rival the work of Mozart; judge a court case with absolute impartiality and fairness; or even converse with the natural ease of your best friend.

From the Rosetta Stone to public-key cryptography, the art and science of cryptology has been used to unlock the vivid history of ancient cultures, to turn the tide of warfare, and to thwart potential hackers from attacking computer systems.

Model Validation and Uncertainty Quantification, Volume 3:  Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021, the third volume of nine from the Conference brings together contributions to this important area of research and engineering.

The successful 30-Second series tackles numbers, with experts on maths and data demystifying the essential numerical topics.

Fuzzy data such as marks, scores, verbal evaluations, imprecise observations, experts' opinions and grey tone pictures, are quite common.

This book is an essay on the epistemology of classifications.

This monograph is intended for an advanced undergraduate or graduate course as well as for researchers, who want a compilation of developments in this rapidly growing field of operations research.

This book serves as a textbook in real analysis.

The main item in the present volume was published in 1930 under the title Das Unendliche in der Mathematik und seine Ausschaltung.

String art is a well-known and popular activity that uses string, a board, and nails to produce artistic images (although there are variations that use different modalities).

A Beginner's Guide to Mathematical Proof prepares mathematics majors for the transition to abstract mathematics, as well as introducing a wider readership of quantitative science students, such as engineers, to the mathematical structures underlying more applied topics.

This bookgathers the proceedings of the conference "e;Cultures of Mathematics andLogic,"e; held in Guangzhou, China.

Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials.

This text is the fifth and final in the series of educational books written by Israel Gelfand with his colleagues for high school students.

Drawing primarily from historical examples, this book explains the tremendous role that numbers and, in particular, mathematics play in all aspects of our civilization and culture.

A systematic logical study of dependence also providing a precise treatment of independence friendly logic.

This textbook gives a comprehensive and modern introduction to mathematical logic at the upper-undergraduate and beginning graduate level.

Logicians have developed beautiful algorithmic techniques for the construction of computably enumerable sets.