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  • Nonlinear Fractional Differential Equations of Variable Order

    The book explores the theory and applications of fractional differential equations with variable order. It delves into the mathematical foundations, including notations, definitions, and key theorems, while also addressing practical applications in various fields. The book will guide readers from basic concepts to advanced topics, making it suitable for both researchers and graduate students in ... Leer más

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    Series series Mathematics and Statistics (R0)
    This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of ... Leer más

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  • Foundations of Modern Analysis

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    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 ... Leer más

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  • A Course in Mathematical Analysis: Volume 1, Foundations and Elementary Real Analysis

    The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This ... Leer más

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  • Course On Abstract Algebra, A (Second Edition)

    This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' notes at the Department of Mathematics, National Chung Cheng University, it contains material sufficient for three semesters of study. It begins with a description of the algebraic structures of the ring of integers and the field of rational numbers. Abstract groups are then ... Leer más

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  • Introduction to Abstract Algebra

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    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 ... Leer más

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  • Understanding Analysis

    Series series Mathematics and Statistics (R0)
    Understanding Analysis outlines an elementary, one-semester course designed to expose students to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on the ... Leer más

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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 ... Leer más

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  • Theories, Sites, Toposes

    Relating and studying mathematical theories through topos-theoretic 'bridges'

    According to Grothendieck, the notion of topos is "the bed or deep river where come to be married geometry and algebra, topology and arithmetic, mathematical logic and category theory, the world of the continuous and that of discontinuous or discrete structures". It is what he had "conceived of most broad to perceive with finesse, by the same language rich of geometric resonances, an "essence" ... Leer más

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  • Algebra 1

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    This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two ... Leer más

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