Mathematical foundations

Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems.

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.

Lectures on Invariant Subspaces grew out of a series of lectures given gave at the University of Uppsala in the spring of 1962, and again in Berkeley the following semester.

Das Buch enthält 185 vollständige chronologisch geordnete Briefe Cantors aus den verschiedenen Perioden seines Lebens, von denen ein großer Teil erstmals veröffentlicht wird.

Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Godel's Theorem, and the Skolem Paradox.

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

A Petri net is a mathematical representation of a network.

In mathematics we are interested in why a particular formula is true.

This textbook teaches everyday mathematics topics to non-math majors at the undergraduate level.

Employs basic mathematical skills to teach students how to address topical, real-world problems using quantitative reasoning.

The study of polynomial completeness of algebraic systems has only recently matured, and until now, lacked a unified treatment.

Resolution Proof Systems: An Algebraic Theory presents a new algebraic framework for the design and analysis of resolution- based automated reasoning systems for a range of non-classical logics.

Working out solutions to polynomial equations is a mathematical problem that dates from antiquity.

The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master.

A logic-based approach to the design of computing systems would, undoubtedly, offer many advantages over the imperative paradigm most commonly applied so far for programming and hardware design and, consequently, logic, again and again, has been heralded as the basis for the next generation of computer systems.

Model theory, a major branch of mathematical logic, plays a key role connecting logic and other areas of mathematics such as algebra, geometry, analysis, and combinatorics.

Convergence of Blockchain, AI and IoT: A Digital Platform discusses the convergence of three powerful technologies that play into the digital revolution and blur the lines between biological, digital, and physical objects.

This volume, first published in 1999, is a valuable resource on combinatorics for graduate students and researchers.

In 1953 I realized that the straight line leads to the downfall of mankind.

'Points, questions, stories, and occasional rants introduce the 24 chapters of this engaging volume.

Philosophy of Mathematics is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods.

Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers.

This monograph began life as a series of papers documenting five years of research into the logical foundations of Categorial Grammar, a grammatical paradigm which has close analogies with Lambda Calculus and Type Theory.

Lowenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that is, the part of logic that concerns the relationship between formal theories and their models.

This volume presents a unified and coherent account of the many and various parts of general recursion theory.

A rigorous introduction to real analysis for undergraduates.

The theory of formal languages is widely recognized as the backbone of theoretical computer science, originating from mathematics and generative linguistics, among others.

This 2006 book addresses the comprehensive introduction to the mathematical principles needed by modern social scientists.

This story of a highly intelligent observer of the turbulent 20th century who was intimately involved as the secretary and bodyguard to Leon Trotsky is based on extensive interviews with the subject, Jean van Heijenoort, and his family, friends, and colleagues.

Cybersecurity Analytics is for the cybersecurity student and professional who wants to learn data science techniques critical for tackling cybersecurity challenges, and for the data science student and professional who wants to learn about cybersecurity adaptations.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.

CHOICE: Highly RecommendedQuarks, Leptons and The Big Bang, Third Edition, is a clear, readable and self-contained introduction to particle physics and related areas of cosmology.

This book explains the first published consistency proof of PA.

Erleben Sie das Wiedererwachen des universitären Lebens nach 1918 aus der Sicht eines Betroffenen.

The visit of Gerald Sacks to the National University of Singapore in 1981 provided an opportunity to organize a shortconference in Mathematical Logic.

Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry.

This book is a useful, attractive introduction to basic counting techniques for upper secondary and junior college students, as well as teachers.

On January 22, 1990, the late John Bell held at CERN (European Laboratory for Particle Physics), Geneva a seminar organized by the Center of Quantum Philosophy, that at this time was an association of scientists interested in the interpretation of quantum mechanics.

Design for security and meet real-time requirements with this must-have book covering basic theory, hardware design and implementation of cryptographic algorithms, and side channel analysis.

A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.

This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena.

This book collects chapters which discuss interdisciplinary solutions to complex problems by using different approaches in order to save money, time and resources.

The second volume of a pair that charts relation algebras from novice to expert level, this text brings the well-grounded reader to the frontiers of research.