Mathematics

Set Theory & Logic

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Beyond First Order Model Theory

Jose Iovino
August 30, 2017

Model theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for...

Exploring the Infinite: An Introduction to Proof and Analysis

Jennifer Brooks
December 16, 2016

Exploring the Infinite addresses the trend toward a combined transition course and introduction to analysis course. It guides the reader through the processes of abstraction and log- ical argumentation, to make the transition from student of mathematics to practitioner of mathematics. This...

A Bridge to Higher Mathematics

Valentin Deaconu, Donald C. Pfaff
December 05, 2016

A Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The...

Handbook of Mathematical Induction: Theory and Applications

David S. Gunderson
November 16, 2016

Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of...

Handbook of Finite State Based Models and Applications

Jiacun Wang
November 16, 2016

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. Handbook of Finite State Based Models and Applications provides a...

Algebra & Geometry: An Introduction to University Mathematics

Mark V. Lawson
May 12, 2016

Algebra & Geometry: An Introduction to University Mathematics provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical...

The Truth Value Algebra of Type-2 Fuzzy Sets: Order Convolutions of Functions on the Unit Interval

John Harding, Carol L. Walker, Elbert A. Walker
March 09, 2016

Type-2 fuzzy sets extend both ordinary and interval-valued fuzzy sets to allow distributions, rather than single values, as degrees of membership. Computations with these truth values are governed by the truth value algebra of type-2 fuzzy sets. The Truth Value Algebra of Type-2 Fuzzy Sets: Order...

Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity

Cyrus F. Nourani
February 24, 2016

This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories...

A Concise Introduction to Pure Mathematics, Fourth Edition

Martin Liebeck
November 03, 2015

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. It covers not only standard material but also many interesting topics not usually...

Introduction to Mathematical Logic, Sixth Edition

Elliott Mendelson
June 08, 2015

The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also...

Application of Fuzzy Logic to Social Choice Theory

John N. Mordeson, Davender S. Malik, Terry D. Clark
March 03, 2015

Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice...

Introduction to Mathematical Proofs, Second Edition

Charles Roberts
December 17, 2014

Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs. Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive...

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