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  • Computable Structures and the Hyperarithmetical Hierarchy

    Series Book 144 - Studies in Logic and the Foundations of Mathematics
    This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there ... Read more

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  • Foundations of Modern Analysis

    by J. Dieudonne ...
    In this text, the whole structure of analysis is built up from the foundations. The only things assumed at the outset are the rules of logic and the usual properties of the natural numbers, and with these two exceptions all the proofs in the text rest on the axioms and theorems proved earlier. Nevertheless this treatise (including the first volume) is not suitable for students who have not yet ... Read more

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  • Real Analysis with Economic Applications

    by Efe A. Ok ...
    There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students.The emphasis throughout is ... Read more

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  • A First Course in Analysis

    Series series Cambridge Mathematical Textbooks
    This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the ... Read more

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  • Introduction to Abstract Algebra

    From Rings, Numbers, Groups, and Fields to Polynomials and Galois Theory

    A new approach to abstract algebra that eases student anxieties by building on fundamentals.Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression ... Read more

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  • Understanding Real Analysis

    by Paul Zorn ...
    Understanding Real Analysis, Second Edition offers substantial coverage of foundational material and expands on the ideas of elementary calculus to develop a better understanding of crucial mathematical ideas. The text meets students at their current level and helps them develop a foundation in real analysis.The author brings definitions, proofs, examples and other mathematical tools together to ... Read more

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  • Introduction To Number Theory

    Series Book 0 - Essential Textbooks In Mathematics
    'Probably its most significant distinguishing feature is that this book is more algebraically oriented than most undergraduate number theory texts.'MAA ReviewsIntroduction to Number Theory is dedicated to concrete questions about integers, to place an emphasis on problem solving by students. When undertaking a first course in number theory, students enjoy actively engaging with the properties and ... Read more

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  • Measures, Integrals and Martingales

    A concise yet elementary introduction to measure and integration theory, which are vital in many areas of mathematics, including analysis, probability, mathematical physics and finance. In this highly successful textbook, core ideas of measure and integration are explored, and martingales are used to develop the theory further. Other topics are also covered such as Jacobi's transformation theorem, ... Read more

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  • Abstract Algebra

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    Series series Mathematics and Statistics (R0)
    This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields.The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite ... Read more

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  • Nonmeasurable Sets and Functions

    Series Book 195 - North-Holland Mathematics Studies
    The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics:1. ... Read more

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  • Analysis on Polish Spaces and an Introduction to Optimal Transportation

    Series Book 89 - London Mathematical Society Student Texts
    A large part of mathematical analysis, both pure and applied, takes place on Polish spaces: topological spaces whose topology can be given by a complete metric. This analysis is not only simpler than in the general case, but, more crucially, contains many important special results. This book provides a detailed account of analysis and measure theory on Polish spaces, including results about spaces ... Read more

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