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Computability: Computable Functions, Logic, and the Foundations of Mathematics
Now in a new edition!--the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with$22.79
The Foundations of Mathematics
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties$71.99
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)
This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz$49.59
Understanding Mathematical Proof
The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs. Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techniques that mathematicians adopt to prove their$58.39
Almost Free Modules: Set-Theoretic Methods
This is an extended treatment of the set-theoretic techniques which have transformed the study of abelian group and module theory over the last 15 years. Part of the book is new work which does not appear elsewhere in any form. In addition, a large body of material which has appeared previously (in scattered and sometimes inaccessible journal articles) has been extensively reworked and in many$51.99
Algebra & Geometry: An Introduction to University Mathematics
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 origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and$85.49
Proceedings of the 13th Asian Logic Conference
This volume provides a forum which highlights new achievements and overviews of recent developments of the thriving logic groups in the Asia-Pacific region. It contains papers by leading logicians and also some contributions in computer science logics and philosophic logics.Contents:An Analogy Between Cardinal Characteristics and Highness Properties of Oracles (Jörg Brendle, Andrew Brooke-Taylor,$33.99
Australian Mathematical Society Lecture Series (Book 21)
This is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All of the standard topics are included, as well as a proper treatment of the trigonometric functions, which