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The description for this book, An Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 18, will be forthcoming.

Functional equations. --- Addition. --- Antiderivative. --- Asymptotic formula. --- Bessel function. --- Beta function. --- Boundary value problem. --- Change of variables. --- Closed-form expression. --- Coefficient. --- Combination. --- Continuous function. --- Corollary. --- Differential equation. --- Enumeration. --- Equation. --- Existential quantification. --- Explicit formula. --- Exponential function. --- Factorial. --- Function (mathematics). --- Functional equation. --- Hermite polynomials. --- Hypergeometric function. --- Integer. --- Laguerre polynomials. --- Laplace transform. --- Legendre function. --- Linear difference equation. --- Linear differential equation. --- Mathematical induction. --- Mathematician. --- Monomial. --- Natural number. --- Number theory. --- Ordinary differential equation. --- Parameter. --- Periodic function. --- Polygamma function. --- Polynomial. --- Potential theory. --- Power series. --- Rectangle. --- Recurrence relation. --- Remainder. --- Scientific notation. --- Sequent. --- Simple function. --- Singular solution. --- Special case. --- Special functions. --- Summation. --- Theorem. --- Theory. --- Uniqueness theorem. --- Variable (mathematics). --- Without loss of generality.

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This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or hyperbolic. This approach to link theory is particularly attractive since most invariants of links are additive under splicing.Specially distinguished from this viewpoint is the class of links, none of whose splice components is hyperbolic. It includes all links constructed by cabling and connected sums, in particular all links of singularities of complex plane curves. One of the main contributions of this monograph is the calculation of invariants of these classes of links, such as the Alexander polynomials, monodromy, and Seifert forms.

Algebraic geometry --- Differential geometry. Global analysis --- Link theory. --- Curves, Plane. --- SINGULARITIES (Mathematics) --- Curves, Plane --- Invariants --- Link theory --- Singularities (Mathematics) --- Geometry, Algebraic --- Low-dimensional topology --- Piecewise linear topology --- Higher plane curves --- Plane curves --- Invariants. --- 3-sphere. --- Alexander Grothendieck. --- Alexander polynomial. --- Algebraic curve. --- Algebraic equation. --- Algebraic geometry. --- Algebraic surface. --- Algorithm. --- Ambient space. --- Analytic function. --- Approximation. --- Big O notation. --- Call graph. --- Cartesian coordinate system. --- Characteristic polynomial. --- Closed-form expression. --- Cohomology. --- Computation. --- Conjecture. --- Connected sum. --- Contradiction. --- Coprime integers. --- Corollary. --- Curve. --- Cyclic group. --- Determinant. --- Diagram (category theory). --- Diffeomorphism. --- Dimension. --- Disjoint union. --- Eigenvalues and eigenvectors. --- Equation. --- Equivalence class. --- Euler number. --- Existential quantification. --- Exterior (topology). --- Fiber bundle. --- Fibration. --- Foliation. --- Fundamental group. --- Geometry. --- Graph (discrete mathematics). --- Ground field. --- Homeomorphism. --- Homology sphere. --- Identity matrix. --- Integer matrix. --- Intersection form (4-manifold). --- Isolated point. --- Isolated singularity. --- Jordan normal form. --- Knot theory. --- Mathematical induction. --- Monodromy matrix. --- Monodromy. --- N-sphere. --- Natural transformation. --- Newton polygon. --- Newton's method. --- Normal (geometry). --- Notation. --- Pairwise. --- Parametrization. --- Plane curve. --- Polynomial. --- Power series. --- Projective plane. --- Puiseux series. --- Quantity. --- Rational function. --- Resolution of singularities. --- Riemann sphere. --- Riemann surface. --- Root of unity. --- Scientific notation. --- Seifert surface. --- Set (mathematics). --- Sign (mathematics). --- Solid torus. --- Special case. --- Stereographic projection. --- Submanifold. --- Summation. --- Theorem. --- Three-dimensional space (mathematics). --- Topology. --- Torus knot. --- Torus. --- Tubular neighborhood. --- Unit circle. --- Unit vector. --- Unknot. --- Variable (mathematics).

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This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed.Originally published in 1986.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Constructive mathematics. --- Arithmetic. --- Mathematics --- Set theory --- Calculators --- Numbers, Real --- Mathematics, Constructive --- Logic, Symbolic and mathematical --- Addition. --- Adjunction (field theory). --- Age of the universe. --- Almost surely. --- Arithmetic IF. --- Atomic formula. --- Axiom. --- Axiomatic system. --- Beta function. --- Big O notation. --- Binary number. --- Binary relation. --- Brownian motion. --- Canonical form. --- Cardinality. --- Cartesian coordinate system. --- Chessboard. --- Classical mathematics. --- Closed-form expression. --- Commutative property. --- Computation. --- Conservative extension. --- Consistency. --- Contradiction. --- Deduction theorem. --- Diameter. --- Direct proof. --- Domain of discourse. --- Elementary mathematics. --- Elias M. Stein. --- Existential quantification. --- Exponential function. --- Exponentiation. --- Extension by definitions. --- Finitary. --- Finite set. --- Formula C (SCCA). --- Foundations of mathematics. --- Fundamenta Mathematicae. --- Gödel's completeness theorem. --- Herbrand's theorem. --- Impredicativity. --- Inaccessible cardinal. --- Inference. --- Interpretability. --- John Milnor. --- Logic. --- Logical connective. --- Mathematical induction. --- Mathematical logic. --- Mathematician. --- Mathematics. --- Measurable cardinal. --- Metamathematics. --- Metatheorem. --- Model theory. --- Mostowski. --- Natural number. --- Negation. --- Non-standard analysis. --- Notation. --- P-adic analysis. --- Peano axioms. --- Polynomial. --- Positional notation. --- Power of two. --- Power set. --- Primitive notion. --- Primitive recursive function. --- Principia Mathematica. --- Probability theory. --- Quantifier (logic). --- Quantity. --- Ranking (information retrieval). --- Rational number. --- Real number. --- Recursion (computer science). --- Remainder. --- Requirement. --- Robert Langlands. --- Rule of inference. --- Scientific notation. --- Sequence. --- Set theory. --- Subset. --- Theorem. --- Theory. --- Transfer principle. --- Transfinite number. --- Triviality (mathematics). --- Tuple. --- Uniqueness. --- Universal quantification. --- Variable (mathematics). --- Zermelo–Fraenkel set theory.

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The description for this book, Existence Theorems in Partial Differential Equations. (AM-23), Volume 23, will be forthcoming.

Differential equations, Partial. --- Existence theorems. --- 0O. --- 3N. --- Addition. --- Analytic function. --- Applied mathematics. --- Big O notation. --- Biharmonic equation. --- Boundary value problem. --- C0. --- Calculation. --- Cartesian coordinate system. --- Cauchy problem. --- Characteristic equation. --- Closed-form expression. --- Coefficient. --- Computation. --- Computational problem. --- Constructive proof. --- Continuous function (set theory). --- Continuous function. --- Convex set. --- Coordinate system. --- Derivative. --- Determination. --- Differential equation. --- Dirichlet problem. --- Elliptic partial differential equation. --- Empty set. --- Equation. --- Existence theorem. --- Existential quantification. --- Explicit formulae (L-function). --- Exterior (topology). --- Finite difference. --- Flattening. --- Formal scheme. --- Fourier transform. --- Fundamental solution. --- Geometry. --- Green's function. --- Harmonic function. --- Implicit function theorem. --- Implicit function. --- Improper integral. --- Initial value problem. --- Integral equation. --- Interval (mathematics). --- Laplace transform. --- Limit of a sequence. --- Linear combination. --- Linear differential equation. --- Linear equation. --- Mathematician. --- Method of characteristics. --- Nonlinear system. --- Numerical analysis. --- Ordinary differential equation. --- Parameter. --- Partial derivative. --- Partial differential equation. --- Pessimism. --- Plane curve. --- Power series. --- Probability of success. --- Probability. --- Pure mathematics. --- Radius of convergence. --- Real number. --- Real variable. --- Requirement. --- Scientific notation. --- Second derivative. --- Series (mathematics). --- Simultaneous equations. --- Special case. --- Terminology. --- Theorem. --- Theory. --- Three-dimensional space (mathematics). --- Truncation error. --- Uniform convergence. --- Upper and lower bounds. --- Variable (mathematics).