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Mathematical Analysis II by Elias Zakon
This final text in the Zakon Series on Mathematics Analysis follows the release of the author's Basic Concepts of Mathematics and Mathematical Analysis I and completes the material on Real Analysis that is the foundation for later courses in function . . . READ MORE
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Real Variables with Basic Metric Space Topology Robert Ash
Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Gear . . . READ MORE
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Mathematical Analysis I, Elias Zakon
This book carefully leads the student through the basic topics of real analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, . . . READ MORE
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Introduction to Mathematical Analysis Beatriz Lafferriere
This set of lecture notes provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after compl . . . READ MORE
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Applied Analysis by John Hunter, Bruno Nachtergaele
This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical r . . . READ MORE
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Basic Concepts of Mathematics by Elias Zakon
This text helps the student complete the transition from purely manipulative to rigorous mathematics. It spells out in all detail what is often treated too briefly or vaguely because of lack of time or space. It can be used either for supplementary r . . . READ MORE
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The Theory Of Integration by L. C. Young
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This book on the one hand, practically no knowledge is assumed (merely what concerns existence of real numbers ,an . . . READ MORE
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Irrational numbers and their representation by sequence
This book is intended to explain the nature of irrational numbers, and those parts of Algebra which depend on what is usually called The Theory of Limits. It explained how the fundamental operations are to be performed in the case of irrational numb . . . READ MORE
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Notes on Measure and Integration by John Franks
This text introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to investigate the standard convergence theorems and a brief introduction to the Hilbert space of L2 functions on the interval. The actual construction o . . . READ MORE
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The Foundations of Analysis by Larry Clifton
This text is a detailed and self-contained introduction to the real number system from a categorical perspective. It begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios as presented in Book V of Euclid, a . . . READ MORE
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The General Theory of Dirichlet's Series by G.H. Hardy
This classic work explains the theory and formulas behind Dirichlet's series and offers the first systematic account of Riesz's theory of the summation of series by typical means. Its authors rank among the most distinguished mathematicians of the tw . . . READ MORE
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A Course of Pure Mathematics by G.H. Hardy
There can be few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergradua . . . READ MORE
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Orders of Infinity by G. H. Hardy
The ideas of Du Bois-Reymond’s Infinit¨arcalc¨ul are of great and growing importance in all branches of the theory of functions. With the particular system of notation that he invented, it is, no doubt, quite possible to dispense; but it can hardly b . . . READ MORE
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Lectures on Lipschitz Analysis by Juha Heinonen
These lectures notes concentrate on the theory of Lipschitz functions in Euclidean spaces. . . . READ MORE
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Elliptic Functions by Arthur Latham Baker (PDF)
Elliptic Functions was the determination of a relation between the amplitudes of three functions of either order, such that there should exist an algebraic relation between the three functions themselves of which these were the amplitudes. It is one . . . READ MORE
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Undergraduate Analysis Tools by Bruce K. Driver
This textbook is on undergraduate analysis tools. It covers topics such as natural, integer, rational and real numbers, as well as fields, complex numbers, metric spaces, and set operations/functions. The document is divided into two parts, with part . . . READ MORE
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Topics in Real and Functional Analysis by Gerald Teschl
This manuscript provides a brief introduction to Real and (linear and nonlinear) Functional Analysis given lecture at the University of Vienna in winter 2004, 2009 and 2011. It covers basic Hilbert and Banach space theory as well as basic measure th . . . READ MORE
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Introduction to Infinitesimal Analysis by N. J. Lennes
This text is dealing with the fundamental theorems of infinitesimal calculus in a rigorous manner is now recognized as an essential part of the training of a mathematician. It appears in the curriculum of nearly every university, and is taken by stud . . . READ MORE
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Homeomorphisms in Analysis by Casper Goffman
This book features the interplay of two main branches of mathematics: topology and real analysis. The material of the book is largely contained in the research publications of the authors and their students from the past 50 years. Parts of analysis a . . . READ MORE
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Introduction to Lebesgue Integration by William Chen
This text is an introduction to some of the basic ideas in Lebesgue integration with the minimal use of measure theory. . . . READ MORE
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Fundamentals of Analysis by William Chen
This set of notes has been organized in such a way to create a single volume suitable for an introduction to some of the basic ideas in analysis.
Chapters 1 - 4 and 7 - 8 were used in various forms and on many occasions between 1982 and 1990 by the . . . READ MORE
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Theory of Functions of a Real Variable Shlomo Sternberg
This text is for a beginning graduate course in real variables and functional analysis. The course assumes that the student has seen the basics of real variable theory and point set topology. . . . READ MORE
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An Introductory Course Of Mathematical Analysis
This textbook was aimed at first-year undergraduates studying physics and chemistry, to help them become acquainted with the concepts and processes of differentiation and integration. Notably, a prominence is given to inequalities and more specifical . . . READ MORE
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