Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

An outrageous graphic novel that investigates key concepts in mathematicsIntegers and permutations-two of the most basic mathematical objects-are born of different fields and analyzed with different techniques. Yet when the Mathematical Sciences Investigation team of crack forensic mathematicians, led by Professor Gauss, begins its autopsies of the victims of two seemingly unrelated homicides, Arnie Integer and Daisy Permutation, they discover the most extraordinary similarities between the structures of each body.Prime Suspects is a graphic novel that takes you on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics.Travel with Detective von Neumann as he leaves no clue unturned, from shepherds' huts in the Pyrenees to secret societies in the cafés of Paris, from the hidden codes in the music of the stones to the grisly discoveries in Finite Fields. Tremble at the ferocity of the believers in deep and rigid abstraction. Feel the pain as you work with our young heroine, Emmy Germain, as she blazes a trail for women in mathematical research and learns from Professor Gauss, the greatest forensic detective of them all.Beautifully drawn and wittily and exquisitely detailed, Prime Suspects is unique, astonishing, and outrageous-a once-in-a-lifetime opportunity to experience mathematics like never before.

Mathematics --- Math --- Science --- Accuracy and precision. --- Alan Turing. --- Alexander Grothendieck. --- Analytic number theory. --- Anatoly Vershik. --- Arithmetic. --- Atle Selberg. --- Ben Green (mathematician). --- Bernhard Riemann. --- Bessel function. --- Big O notation. --- Binary logarithm. --- Bryna Kra. --- Calculation. --- Child prodigy. --- Coefficient. --- Comic book. --- Conjecture. --- Coprime integers. --- Cryptography. --- David Hilbert. --- Diagram (category theory). --- Diophantine geometry. --- Diophantus. --- Disquisitiones Arithmeticae. --- Emil Artin. --- Emmy Noether. --- Enrico Bombieri. --- Erica Klarreich. --- Felix Klein. --- Fermat's Last Theorem. --- Fields Medal. --- Friedrich Bessel. --- Fundamental theorem of arithmetic. --- Gamma function. --- Gauss sum. --- Gelfand. --- Grigori Perelman. --- Henri Cartan. --- Hermann Weyl. --- Hilbert's tenth problem. --- Integer. --- Jean-Pierre Serre. --- Joint probability distribution. --- Julia Robinson. --- Keith Devlin. --- Klaus Roth. --- Kloosterman sum. --- Language of mathematics. --- Logarithm. --- Log-log plot. --- Manjul Bhargava. --- Maryam Mirzakhani. --- Mathematical problem. --- Mathematical sciences. --- Mathematician. --- Mathematics. --- Men of Mathematics. --- Millennium Prize Problems. --- Modular form. --- Monic polynomial. --- Multiplication table. --- Natural logarithm. --- Natural number. --- Nicolas Bourbaki. --- Normal distribution. --- Number theory. --- Occam's razor. --- Oswald Veblen. --- Parity (mathematics). --- Permutation. --- Persi Diaconis. --- Peter Gustav Lejeune Dirichlet. --- Peter Scholze. --- Pierre Deligne. --- Pierre Samuel. --- Plus-minus sign. --- Poisson distribution. --- Polynomial. --- Prime factor. --- Prime number. --- Prime power. --- Probability theory. --- Proportionality (mathematics). --- Pure mathematics. --- Random permutation. --- Richard Dedekind. --- Riemann hypothesis. --- Riemann surface. --- Riemann zeta function. --- Robin Hartshorne. --- Saunders Mac Lane. --- Serge Lang. --- Shinichi Mochizuki. --- Siegel zero. --- Sieve theory. --- Sophie Germain. --- Stirling numbers of the first kind. --- Summation. --- Variable (mathematics).

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The classic book that shares the enjoyment of mathematics with readers of all skill levelsWhat is so special about the number 30? Do the prime numbers go on forever? Are there more whole numbers than even numbers? The Enjoyment of Math explores these and other captivating problems and puzzles, introducing readers to some of the most fundamental ideas in mathematics. Written by two eminent mathematicians and requiring only a background in plane geometry and elementary algebra, this delightful book covers topics such as the theory of sets, the four-color problem, regular polyhedrons, Euler’s proof of the infinitude of prime numbers, and curves of constant breadth. Along the way, it discusses the history behind the problems, carefully explaining how each has arisen and, in some cases, how to resolve it. With an incisive foreword by Alex Kontorovich, this Princeton Science Library edition shares the enjoyment of math with a new generation of readers.

Mathematics --- Mathematical recreations. --- Mathematical puzzles --- Number games --- Recreational mathematics --- Recreations, Mathematical --- Puzzles --- Scientific recreations --- Games in mathematics education --- Magic squares --- Magic tricks in mathematics education --- Arbitrarily large. --- Arithmetic. --- Big O notation. --- Binomial theorem. --- Bonse's inequality. --- Circumference. --- Coefficient. --- Combination. --- Complete theory. --- Computation. --- Coprime integers. --- Diameter. --- Divisor. --- Equilateral triangle. --- Euler's formula. --- Euler's theorem. --- Exterior (topology). --- Factorial. --- Factorization. --- Fermat's Last Theorem. --- Fermat's theorem. --- Fourth power. --- Fractional part. --- Geometric mean. --- Geometric series. --- Geometry. --- Hypotenuse. --- Integer factorization. --- Intersection (set theory). --- Irrational number. --- Line segment. --- Logarithm. --- Long division. --- Mathematical induction. --- Mathematics. --- Metric space. --- Natural number. --- Non-Euclidean geometry. --- Number theory. --- Parallelogram. --- Parity (mathematics). --- Pedal triangle. --- Perfect number. --- Polyhedron. --- Power of 10. --- Prime factor. --- Prime number theorem. --- Prime number. --- Prime power. --- Pure mathematics. --- Pythagorean theorem. --- Rational number. --- Rectangle. --- Regular polygon. --- Regular polyhedron. --- Remainder. --- Reuleaux triangle. --- Rhomboid. --- Rhombus. --- Right angle. --- Right triangle. --- Scientific notation. --- Sign (mathematics). --- Special case. --- Straightedge. --- Summation. --- Theorem. --- Transfinite number. --- Variable (mathematics). --- Waring's problem.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The ∂̄ Neumann problem is probably the most important and natural example of a non-elliptic boundary value problem, arising as it does from the Cauchy-Riemann equations. It has been known for some time how to prove solvability and regularity by the use of L2 methods. In this monograph the authors apply recent methods involving the Heisenberg group to obtain parametricies and to give sharp estimates in various function spaces, leading to a better understanding of the ∂̄ Neumann problem. The authors have added substantial background material to make the monograph more accessible to students.Originally published in 1977.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.

Partial differential equations --- Neumann problem. --- Neumann problem --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Boundary value problems --- Differential equations, Partial --- A priori estimate. --- Abuse of notation. --- Analytic continuation. --- Analytic function. --- Approximation. --- Asymptotic expansion. --- Asymptotic formula. --- Basis (linear algebra). --- Besov space. --- Boundary (topology). --- Boundary value problem. --- Boundedness. --- Calculation. --- Cauchy's integral formula. --- Cauchy–Riemann equations. --- Change of variables. --- Characterization (mathematics). --- Combination. --- Commutative property. --- Commutator. --- Complex analysis. --- Complex manifold. --- Complex number. --- Computation. --- Convolution. --- Coordinate system. --- Corollary. --- Counterexample. --- Derivative. --- Determinant. --- Differential equation. --- Dimension (vector space). --- Dimension. --- Dimensional analysis. --- Dirichlet boundary condition. --- Eigenvalues and eigenvectors. --- Elliptic boundary value problem. --- Equation. --- Error term. --- Estimation. --- Even and odd functions. --- Existential quantification. --- Function space. --- Fundamental solution. --- Green's theorem. --- Half-space (geometry). --- Hardy's inequality. --- Heisenberg group. --- Holomorphic function. --- Infimum and supremum. --- Integer. --- Integral curve. --- Integral expression. --- Inverse function. --- Invertible matrix. --- Iteration. --- Laplace's equation. --- Left inverse. --- Lie algebra. --- Lie group. --- Linear combination. --- Logarithm. --- Lp space. --- Mathematical induction. --- Neumann boundary condition. --- Notation. --- Open problem. --- Orthogonal complement. --- Orthogonality. --- Parametrix. --- Partial derivative. --- Pointwise. --- Polynomial. --- Principal branch. --- Principal part. --- Projection (linear algebra). --- Pseudo-differential operator. --- Quantity. --- Recursive definition. --- Schwartz space. --- Scientific notation. --- Second derivative. --- Self-adjoint. --- Singular value. --- Sobolev space. --- Special case. --- Standard basis. --- Stein manifold. --- Subgroup. --- Subset. --- Summation. --- Support (mathematics). --- Tangent bundle. --- Theorem. --- Theory. --- Upper half-plane. --- Variable (mathematics). --- Vector field. --- Volume element. --- Weak solution. --- Neumann, Problème de --- Equations aux derivees partielles --- Problemes aux limites

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early 1980s, Robert Coleman discovered a way to construct primitives of analytic one-forms on certain smooth p-adic analytic curves in a bigger class of functions. Since then, there have been several attempts to generalize his ideas to smooth p-adic analytic spaces of higher dimension, but the spaces considered were invariably associated with algebraic varieties. This book aims to show that every smooth p-adic analytic space is provided with a sheaf of functions that includes all analytic ones and satisfies a uniqueness property. It also contains local primitives of all closed one-forms with coefficients in the sheaf that, in the case considered by Coleman, coincide with those he constructed. In consequence, one constructs a parallel transport of local solutions of a unipotent differential equation and an integral of a closed one-form along a path so that both depend nontrivially on the homotopy class of the path. Both the author's previous results on geometric properties of smooth p-adic analytic spaces and the theory of isocrystals are further developed in this book, which is aimed at graduate students and mathematicians working in the areas of non-Archimedean analytic geometry, number theory, and algebraic geometry.

p-adic analysis. --- Analysis, p-adic --- Algebra --- Calculus --- Geometry, Algebraic --- Abelian category. --- Acting in. --- Addition. --- Aisle. --- Algebraic closure. --- Algebraic curve. --- Algebraic structure. --- Algebraic variety. --- Allegory (category theory). --- Analytic function. --- Analytic geometry. --- Analytic space. --- Archimedean property. --- Arithmetic. --- Banach algebra. --- Bertolt Brecht. --- Buttress. --- Centrality. --- Clerestory. --- Commutative diagram. --- Commutative property. --- Complex analysis. --- Contradiction. --- Corollary. --- Cosmetics. --- De Rham cohomology. --- Determinant. --- Diameter. --- Differential form. --- Dimension (vector space). --- Divisor. --- Elaboration. --- Embellishment. --- Equanimity. --- Equivalence class (music). --- Existential quantification. --- Facet (geometry). --- Femininity. --- Finite morphism. --- Formal scheme. --- Fred Astaire. --- Functor. --- Gavel. --- Generic point. --- Geometry. --- Gothic architecture. --- Homomorphism. --- Hypothesis. --- Imagery. --- Injective function. --- Irreducible component. --- Iterated integral. --- Linear combination. --- Logarithm. --- Marni Nixon. --- Masculinity. --- Mathematical induction. --- Mathematics. --- Mestizo. --- Metaphor. --- Morphism. --- Natural number. --- Neighbourhood (mathematics). --- Neuroticism. --- Noetherian. --- Notation. --- One-form. --- Open set. --- P-adic Hodge theory. --- P-adic number. --- Parallel transport. --- Patrick Swayze. --- Phrenology. --- Politics. --- Polynomial. --- Prediction. --- Proportion (architecture). --- Pullback. --- Purely inseparable extension. --- Reims. --- Requirement. --- Residue field. --- Rhomboid. --- Roland Barthes. --- Satire. --- Self-sufficiency. --- Separable extension. --- Sheaf (mathematics). --- Shuffle algebra. --- Subgroup. --- Suggestion. --- Technology. --- Tensor product. --- Theorem. --- Transept. --- Triforium. --- Tubular neighborhood. --- Underpinning. --- Writing. --- Zariski topology.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes.

Markov processes. --- Stochastic difference equations. --- Itō, Kiyosi, --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Itō, K. --- Ito, Kiesi, --- Itō, Kiyoshi, --- 伊藤淸, --- 伊藤清, --- Itō, Kiyosi, --- Itō, Kiyosi, 1915-2008. --- Stochastic difference equations --- Difference equations --- Stochastic processes --- Abelian group. --- Addition. --- Analytic function. --- Approximation. --- Bernhard Riemann. --- Bounded variation. --- Brownian motion. --- Central limit theorem. --- Change of variables. --- Coefficient. --- Complete metric space. --- Compound Poisson process. --- Continuous function (set theory). --- Continuous function. --- Convergence of measures. --- Convex function. --- Coordinate system. --- Corollary. --- David Hilbert. --- Decomposition theorem. --- Degeneracy (mathematics). --- Derivative. --- Diffeomorphism. --- Differentiable function. --- Differentiable manifold. --- Differential equation. --- Differential geometry. --- Dimension. --- Directional derivative. --- Doob–Meyer decomposition theorem. --- Duality principle. --- Elliptic operator. --- Equation. --- Euclidean space. --- Existential quantification. --- Fourier transform. --- Function space. --- Functional analysis. --- Fundamental solution. --- Fundamental theorem of calculus. --- Homeomorphism. --- Hölder's inequality. --- Initial condition. --- Integral curve. --- Integral equation. --- Integration by parts. --- Invariant measure. --- Itô calculus. --- Itô's lemma. --- Joint probability distribution. --- Lebesgue measure. --- Linear interpolation. --- Lipschitz continuity. --- Local martingale. --- Logarithm. --- Markov chain. --- Markov process. --- Markov property. --- Martingale (probability theory). --- Normal distribution. --- Ordinary differential equation. --- Ornstein–Uhlenbeck process. --- Polynomial. --- Principal part. --- Probability measure. --- Probability space. --- Probability theory. --- Pseudo-differential operator. --- Radon–Nikodym theorem. --- Representation theorem. --- Riemann integral. --- Riemann sum. --- Riemann–Stieltjes integral. --- Scientific notation. --- Semimartingale. --- Sign (mathematics). --- Special case. --- Spectral sequence. --- Spectral theory. --- State space. --- State-space representation. --- Step function. --- Stochastic calculus. --- Stochastic. --- Stratonovich integral. --- Submanifold. --- Support (mathematics). --- Tangent space. --- Tangent vector. --- Taylor's theorem. --- Theorem. --- Theory. --- Topological space. --- Topology. --- Translational symmetry. --- Uniform convergence. --- Variable (mathematics). --- Vector field. --- Weak convergence (Hilbert space). --- Weak topology.