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The description for this book, Contributions to Fourier Analysis. (AM-25), will be forthcoming.

Fourier analysis. --- Analysis, Fourier --- Mathematical analysis --- Absolute value. --- Almost periodic function. --- Approximation. --- Bessel function. --- Bilinear map. --- Boundary value problem. --- Characterization (mathematics). --- Coefficient. --- Compact space. --- Comparison theorem. --- Conservative vector field. --- Constant function. --- Continuous function. --- Corollary. --- Counterexample. --- Diagonalization. --- Diagram (category theory). --- Diameter. --- Dimension. --- Dirichlet kernel. --- Dirichlet problem. --- Dirichlet's principle. --- Distribution function. --- Exponential polynomial. --- Exponential sum. --- Fourier series. --- Fourier transform. --- Harmonic function. --- Hilbert space. --- Hölder's inequality. --- Integer. --- Interpolation theorem. --- Linear combination. --- Lp space. --- Measurable function. --- Measure (mathematics). --- Partial derivative. --- Partial differential equation. --- Periodic function. --- Poisson formula. --- Polynomial. --- Power series. --- Quantity. --- Rectangle. --- Remainder. --- Semicircle. --- Several complex variables. --- Sign (mathematics). --- Simple function. --- Special case. --- Sphere. --- Square root. --- Step function. --- Subsequence. --- Subset. --- Theorem. --- Theory. --- Triangle inequality. --- Two-dimensional space. --- Uniform continuity. --- Uniform convergence. --- Variable (mathematics). --- Vector field. --- Vector space.

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In The Structure of Affine Buildings, Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions, and residues of these buildings. It also includes tables correlating the results in the locally finite case with the results of Tits's classification of absolutely simple algebraic groups defined over a local field. A companion to Weiss's The Structure of Spherical Buildings, The Structure of Affine Buildings is organized around the classification of spherical buildings and their root data as it is carried out in Tits and Weiss's Moufang Polygons.

Buildings (Group theory) --- Moufang loops --- Automorphisms --- Affine algebraic groups --- Moufang loops. --- Automorphisms. --- Affine algebraic groups. --- Algebraic groups, Affine --- Loops, Moufang --- Theory of buildings (Group theory) --- Tits's theory of buildings (Group theory) --- Group schemes (Mathematics) --- Group theory --- Symmetry (Mathematics) --- Loops (Group theory) --- Linear algebraic groups --- Buildings (Group theory). --- Addition. --- Additive group. --- Additive inverse. --- Algebraic group. --- Algebraic structure. --- Ambient space. --- Associative property. --- Automorphism. --- Big O notation. --- Bijection. --- Bilinear form. --- Bounded set (topological vector space). --- Bounded set. --- Calculation. --- Cardinality. --- Cauchy sequence. --- Commutative property. --- Complete graph. --- Complete metric space. --- Composition algebra. --- Connected component (graph theory). --- Consistency. --- Continuous function. --- Coordinate system. --- Corollary. --- Coxeter group. --- Coxeter–Dynkin diagram. --- Diagram (category theory). --- Diameter. --- Dimension. --- Discrete valuation. --- Division algebra. --- Dot product. --- Dynkin diagram. --- E6 (mathematics). --- E7 (mathematics). --- E8 (mathematics). --- Empty set. --- Equipollence (geometry). --- Equivalence class. --- Equivalence relation. --- Euclidean geometry. --- Euclidean space. --- Existential quantification. --- Free monoid. --- Fundamental domain. --- Hyperplane. --- Infimum and supremum. --- Jacques Tits. --- K0. --- Linear combination. --- Mathematical induction. --- Metric space. --- Multiple edges. --- Multiplicative inverse. --- Number theory. --- Octonion. --- Parameter. --- Permutation group. --- Permutation. --- Pointwise. --- Polygon. --- Projective line. --- Quadratic form. --- Quaternion. --- Remainder. --- Root datum. --- Root system. --- Scientific notation. --- Sphere. --- Subgroup. --- Subring. --- Subset. --- Substructure. --- Theorem. --- Topology of uniform convergence. --- Topology. --- Torus. --- Tree (data structure). --- Tree structure. --- Two-dimensional space. --- Uniform continuity. --- Valuation (algebra). --- Vector space. --- Without loss of generality.

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More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway to higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth. Now with a new preface by the author, this book documents the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching-a story of genius triumphing over some of the toughest, subtlest problems imaginable. In touring The Calculus Gallery, we can see how it all came to be.

Calculus --- History. --- Absolute value. --- Addition. --- Algebraic number. --- Antiderivative. --- Arc length. --- Augustin-Louis Cauchy. --- Baire category theorem. --- Bernhard Riemann. --- Binomial theorem. --- Bounded function. --- Calculation. --- Central limit theorem. --- Characterization (mathematics). --- Coefficient. --- Complex analysis. --- Continuous function (set theory). --- Continuous function. --- Contradiction. --- Convergent series. --- Corollary. --- Countable set. --- Counterexample. --- Dense set. --- Derivative. --- Diagram (category theory). --- Dichotomy. --- Differentiable function. --- Differential calculus. --- Differential equation. --- Division by zero. --- Equation. --- Existential quantification. --- Fluxion. --- Fourier series. --- Fundamental theorem. --- Geometric progression. --- Geometric series. --- Geometry. --- Georg Cantor. --- Gottfried Wilhelm Leibniz. --- Harmonic series (mathematics). --- Henri Lebesgue. --- Infimum and supremum. --- Infinitesimal. --- Infinity. --- Integer. --- Integration by parts. --- Intermediate value theorem. --- Interval (mathematics). --- Joseph Fourier. --- Karl Weierstrass. --- L'Hôpital's rule. --- Lebesgue integration. --- Lebesgue measure. --- Length. --- Leonhard Euler. --- Limit of a sequence. --- Logarithm. --- Mathematical analysis. --- Mathematician. --- Mathematics. --- Mean value theorem. --- Measurable function. --- Natural number. --- Notation. --- Nowhere continuous function. --- Number theory. --- Pointwise. --- Polynomial. --- Power rule. --- Princeton University Press. --- Q.E.D. --- Quadratic. --- Quantity. --- Rational number. --- Real analysis. --- Real number. --- Rectangle. --- Riemann integral. --- Root test. --- Scientific notation. --- Series (mathematics). --- Set theory. --- Sign (mathematics). --- Stone–Weierstrass theorem. --- Subset. --- Subtangent. --- Summation. --- Tangent. --- Textbook. --- Theorem. --- Theory. --- Transcendental number. --- Trigonometric functions. --- Uniform continuity. --- Uniform convergence. --- Unit interval. --- Upper and lower bounds. --- Vito Volterra. --- Westmont College.