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This text places emphasis on continued fraction Cantor sets and the Hausdorff dimension, algorithms and analysis of algorithms, and multi-dimensional algorithms for simultaneous diophantine approximation. Various computer-generated graphics are presented, and the underlying algorithms are discussed.

Continued fractions. --- Series. --- Algebra --- Mathematics --- Processes, Infinite --- Sequences (Mathematics) --- Fractions, Continued --- Series --- Number theory

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Mathematics --- Number theory --- Sequences (Mathematics) --- History --- Euler, Leonhard, --- 51 <09> --- Mathematics--Geschiedenis van ... --- 51 <09> Mathematics--Geschiedenis van ... --- Mathematical sequences --- Numerical sequences --- Algebra --- Number study --- Numbers, Theory of --- Math --- Science --- Mathematics--Geschiedenis van .. --- Euler, Leonhard --- Mathematics--Geschiedenis van . --- Mathematics--Geschiedenis van --- Mathematics - History - 18th century --- Number theory - History - 18th century --- Sequences (Mathematics) - History - 18th century --- Mathematics - History - 19th century --- Number theory - History - 19th century --- Sequences (Mathematics) - History - 19th century --- Euler, Leonhard, - 1707-1783

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The algebra of primary cohomology operations computed by the well-known Steenrod algebra is one of the most powerful tools of algebraic topology. This book computes the algebra of secondary cohomology operations which enriches the structure of the Steenrod algebra in a new and unexpected way. The book solves a long-standing problem on the algebra of secondary cohomology operations by developing a new algebraic theory of such operations. The results have strong impact on the Adams spectral sequence and hence on the computation of homotopy groups of spheres.

Algebra, Homological. --- Cohomology operations. --- Sequences (Mathematics) --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- Operations (Algebraic topology) --- Algebraic topology --- Homological algebra --- Algebra, Abstract --- Homology theory --- Algebra. --- Algebraic topology. --- Algebraic Topology. --- Topology --- Mathematical analysis

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This book provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. Throughout the book, the authors highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps students get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis. The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs. This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature.

Calculus --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Global analysis (Mathematics). --- Mathematics. --- Sequences (Mathematics). --- Analysis. --- Real Functions. --- Sequences, Series, Summability. --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Math --- Science --- Analysis (Mathematics). --- Functions of real variables. --- Real variables

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A collection of the various old and new results, centered around the following simple observation of J L Walsh. This book is particularly useful for researchers in approximation and interpolation theory.

Polynomials. --- Mathematics. --- Math --- Science --- Algebra --- Global analysis (Mathematics). --- Functions of complex variables. --- Sequences (Mathematics). --- Differential equations, partial. --- Approximations and Expansions. --- Analysis. --- Functions of a Complex Variable. --- Sequences, Series, Summability. --- Several Complex Variables and Analytic Spaces. --- Partial differential equations --- Mathematical sequences --- Numerical sequences --- Mathematics --- Complex variables --- Elliptic functions --- Functions of real variables --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Approximation theory. --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Geometry, Infinitesimal