Set theory

Model theory investigates mathematical structures by means of formal languages.

The book is intended to serve as an introductory course in group theory geared towards second-year university students.

This book features a unique approach to the teaching of mathematical logic by putting it in the context of the puzzles and paradoxes of common language and rational thought.

Naive Set Theory: A Rigorous Approach aims to provide a complete and unitary presentation of naive set theory as the foundation of the whole mathematics.

Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems.

The book is intended to serve as an introductory course in group theory geared towards second-year university students.

Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Fourth Edition presents some of the most fundamental and beautiful ideas in pure mathematics.

The two works titled "e;What Are and What Should the Numbers Be?

This volume presents a novel approach to set theory that is entirely operational.

Fuzzy set theory provides us with a framework which is wider than that of classical set theory.

The fractional Laplacian, also called the Riesz fractional derivative, describes an unusual diffusion process associated with random excursions.

This volume presents the proceedings of the 2000 European Summer Meeting of the Association for Symbolic Logic, marking one hundred years since Hilbert''s famous lecture.

The Art of Proving Binomial Identities accomplishes two goals: (1) It provides a unified treatment of the binomial coefficients, and (2) Brings together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients).

Helps students transition from problem solving to proving theorems, with a new chapter on number theory and over 150 new exercises.

Set theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic.

This is an introductory undergraduate textbook in set theory.

Discrete Mathematics: An Open Introduction, Fourth Edition aims to provide an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math and computer science majors, especially those who intend to teach middle and high school mathematics.

The Banach–Tarski Paradox seems patently false.

This book presents and defends an original and paradigm-shifting conception of formal science, natural science, and the natural universe alike, that's fully pro-science, but at the same time neither theological or God-centered, nor solipsistic or self-centered, nor communitarian or social-institution-centered, nor scientistic or science-valorizing, nor materialist/physicalist or reductive, nor-above all-mechanistic.

The contents in this volume are based on the program Sets and Computations that was held at the Institute for Mathematical Sciences, National University of Singapore from 30 March until 30 April 2015.

This book offers a new, algebraic, approach to set theory.

This volume presents the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Helsinki, Finland in August, 2003.

Transition to Real Analysis with Proof provides undergraduate students with an introduction to analysis including an introduction to proof.

Nonlinear systems with stationary sets are important because they cover a lot of practical systems in engineering.

This textbook gives students a comprehensive introduction to formal methods and their application in software and hardware specification and verification.

This monograph is a testament to the potency of the method of singular integrals of layer potential type in solving boundary value problems for weakly elliptic systems in the setting of Muckenhoupt-weighted Morrey spaces and their pre-duals.

These notes develop the theory of descriptive sets, leading up to a new proof of Louveau''s separation theorem for analytic sets.

Limits of Computation: An Introduction to the Undecidable and the Intractable offers a gentle introduction to the theory of computational complexity.

The authors have written an introduction to logic taking Godel's incompleteness theorem as a starting point.

The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures.

Irrationality and Transcendence in Number Theory tells the story of irrational numbers from their discovery in the days of Pythagoras to the ideas behind the work of Baker and Mahler on transcendence in the 20th century.

This book presents articles of L.

Introduction to Math Olympiad Problems aims to introduce high school students to all the necessary topics that frequently emerge in international Math Olympiad competitions.

This book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors.

Applicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering.

Limits of Computation: An Introduction to the Undecidable and the Intractable offers a gentle introduction to the theory of computational complexity.

Based on lax-algebraic and categorical methods, Monoidal Topology provides a unified theory for metric and topological structures with far-reaching applications.

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

This book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors.

Based on lax-algebraic and categorical methods, Monoidal Topology provides a unified theory for metric and topological structures with far-reaching applications.

Ancient times witnessed the origins of the theory of continued fractions.

This compilation of papers presented at the 2000 European Summer Meeting of the Association for Symbolic Logic marks the centenial anniversery of Hilbert's famous lecture.