Search results for ""mp-amm american mathematical""

Introduces algebraic geometric coding theory. This book covers linear codes, including cyclic codes, and both bounds and asymptotic bounds on the parameters of codes. Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors.

Read more less

Offers a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. This title introduces a class of stratified spaces, so-called stratifolds. It derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality.

Read more less

Suitable for those who wish to explore elementary methods in modern number theory, this book offers an introduction to elementary prime number theory, including Dirichlet's theorem on primes in arithmetic progressions, the Brun sieve, and the Erdos-Selberg proof of the prime number theorem.

Read more less

Mathematical modelling is a subject without boundaries. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. It is suitable for a one-term course for advanced undergraduates.

Read more less

This book, together with the companion volume, Fermat's Last Theorem: The Proof, presents in full detail the proof of Fermat's Last Theorem given by Wiles and Taylor. With these two books, the reader will be able to see the whole picture of the proof to appreciate one of the deepest achievements in the history of mathematics.

Read more less

Symplectic geometry and the theory of Fourier integral operators are modern manifestations of themes that have occupied a central position in mathematical thought. This book intends to develop these themes, and present some of the advances, using the language of differential geometry as a unifying influence.

Read more less

Presents two essential and apparently unrelated subjects that include, microlocal analysis and the theory of pseudo-differential operators, a basic tool in the study of partial differential equations and in analysis on manifolds; and the Nash-Moser theorem, that is fundamentally important in geometry, dynamical systems, and nonlinear PDE.

Read more less

In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works.

Read more less

Contains a variety of results advancing the theory of finite fields and connections with, as well as impact on, various directions in number theory, algebra, and algebraic geometry. Areas of application include algebraic coding theory, cryptology, and combinatorial design theory.

Read more less

Starts with necessary information about matrices, algebras, and groups. This title then proceeds to representations of finite groups. It includes several chapters dealing with representations and characters of symmetric groups and the closely related theory of symmetric polynomials.

Read more less

'The International Conference on Hyperbolic Problems: Theory, Numerics and Applications', 'HYP2008', was held at the University of Maryland from June 9-14, 2008. This title contains articles that cover a range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of 'hyperbolic PDEs'.

Read more less

One of the most active areas in mathematics is the topic of 'additive combinatorics'. This book brings together key researchers from different areas, sharing their insights in articles meant to inspire mathematicians coming from various backgrounds.

Read more less

An introduction to stochastic processes studying certain elementary continuous-time processes. It includes a description of the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a finite number of jumps.

Read more less

Introduces a new notion of analytic space over a non-Archimedean field. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space.

Read more less

Describes in monograph form important applications in numerical methods of linear algebra. This book studies the behavior of the resolvent of a matrix under the perturbation by low rank matrices. It also introduces the basics of value distribution theory of meromorphic scalar functions.

Read more less

Presents an overview of nonlinear conversation laws. This book describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations. It is suitable for researchers and advanced graduate students in the areas of nonlinear partial differential equations and nonlinear analysis.

Read more less

Euler is one of the greatest and most prolific mathematicians of all time. This book examines his work and its relation to current mathematics. It also treats the progression of ideas regarding divergent series from Euler to many parts of modern analysis and quantum physics.

Read more less

Presents an introduction to the theory of quantum computing. This book starts with the basics of classical theory of computation: Turing machines, Boolean circuits, parallel algorithms, probabilistic computation, NP-complete problems, and the idea of complexity of an algorithm. It provides an exposition of quantum computation theory.

Read more less

Presents an exposition of fixed point theory. This work focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property. It aims to show how fixed point theory uses combinatorial ideas related to decomposition of figures into distinct parts called faces, which adjoin each other in a regular fashion.

Read more less

Focuses on the spectral theory for evolution operators and evolution semigroups, a subject tracing its origins to the classical results of J Mather on hyperbolic dynamical systems and J Howland on nonautonomous Cauchy problems. This book includes a collection of examples from different areas of analysis, PDEs, and dynamical systems.

Read more less

Calculus is a powerful tool because it allows us to approximate complicated functions with simpler ones. Indeed, replacing a function locally with a linear - or higher order - approximation is at the heart of calculus. Emphasizing the role of approximations in calculus, this book addresses topics such as derivatives, integrals, and sequences.

Read more less

Modular forms appear in many ways in number theory. This book details various roles that modular forms and $q$-series play in number theory, such as applications and connections to basic hypergeometric functions, Gaussian hypergeometric functions, super-congruences, Weierstrass points on modular curves, singular moduli, and class numbers.

Read more less

Covers Diophantine analysis. Besides the familiar cases of Diophantine equations, this book also covers partitions, representations as a sum of two, three, four or $n$ squares, Waring's problem in general and Hilbert's solution of it, and perfect squares in arithmetical and geometrical progressions.

Read more less

Leads readers to discover some real mathematics. This book is suitable for a one-semester course at the beginning undergraduate level.

Read more less

Emphasizes on functions rather than on geometric or physical applications.

Read more less

Discusses the differential geometric aspects of complex manifolds. This work contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. It discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles. It also gives a brief account of the surface classification theory.

Read more less

Crisscross, zigzag, bowtie, devil, angel, or star: which are the longest, the shortest, the strongest, and the weakest lacings? This book presents the mathematics of shoelaces which is a mix of combinatorics and elementary calculus.

Read more less

Gives a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors have also attempted to give the appropriate references so that the reader may further pursue the statements and proofs of the various results.

Read more less

Focuses on geometry, topology, and partial differential equations. This book discusses a variety of topics, including expository articles on topics such as gauge theory, the Kakeya needle problem, and the Black-Scholes equation. It is suitable for graduate students and research mathematicians interested in broad exposure to mathematical topics.

Read more less

Covers the basic probability of distributions with an emphasis on applications from the areas of investments, insurance, and engineering. This book is suitable as a text for senior undergraduate and beginning graduate students in mathematics, statistics, actuarial science, finance, or engineering.

Read more less

Focusing on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields the topics covered in this volume include Schoof's $\ell$-adic point counting algorithm, the $p$-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on the Jacobians of $C_{ab}$ curves and zeta functions.

Read more less

Examines the theory of measures having values in Banach spaces. This book deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. It also concentrates on measurable vector valued functions and the Bochner integral.

Read more less

Contains 10 articles that explores topics ranging from Fermat's Last Theorem to Computational Fluid Dynamics. This volume includes articles on: a fresh mathematical method that's taking Wall Street by storm 'Ultra-parallel' supercomputing with DNA, and how a mathematician found the famous flaw in the Pentium chip.

Read more less

Presents a basic collection of principles, techniques, and applications needed to conduct independent research in gauge theory and its use in geometry and topology. This title includes self-contained computations of the Seiberg-Witten invariants of most simply connected algebraic surfaces using Witten's factorization method.

Read more less

Describes the properties of harmonic and caloric measures in Lipschitz domains, a relation between parallel surfaces and elliptic equations, monotonicity formulas and rigidity. This book is suitable for graduate students and researchers interested in partial differential equations.

Read more less

Contains lectures from the CBMS Regional Conference held at Harvey Mudd College, June 1977. This monograph consists of applications to nonlinear differential equations of the author's coincidental degree. It includes an bibliography covering many aspects of the modern theory of nonlinear differential equations and the theory of nonlinear analysis.

Read more less

By studying algebraic varieties over a field, this book demonstrates how the notion of schemes is necessary in algebraic geometry. It gives a definition of schemes and describes some of their elementary properties.

Read more less

Presents an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide an account of the introductory portions of this important and technically difficult subject.

Read more less

Uses the theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the analysis of algorithms.

Read more less

Contains papers written by participants of the special session on value distribution theory and complex dynamics held in Hong Kong at the First Joint International Meeting of the AMS and the Hong Kong Mathematical Society in December 2000. This book discusses non-Archimedean analogs of Picard's theorems.

Read more less

Leads readers to discover some real mathematics. This book is suitable for a one-semester course at the beginning undergraduate level.

Read more less

A translation from the Latin of the third and last edition of ""Waring's Meditationes Algebraicae"".

Read more less