Choose an application

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

This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics, which makes intense use of the most advanced concepts from each discipline. In each contribution, the authors give pedagogical introductions to the main concepts underlying their present research and present a personal perspective on some of the most exciting open problems. Keeping this diverse audience in mind, special efforts have been made to ensure that the basic concepts underlying quantum information are covered in an understandable way for mathematical readers, who can find new open challenges for their research. At the same time, the volume will also be of use to physicists wishing to learn advanced mathematical tools, especially those of a differential and algebraic geometric nature.

Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Geometry, algebraic. --- Global differential geometry. --- Quantum Computing. --- Algebraic Geometry. --- Differential Geometry. --- Geometry, Differential --- Algebraic geometry --- Geometry --- Quantum computers. --- Algebraic geometry. --- Differential geometry. --- Differential geometry --- Computers --- Geometry, Algebraic. --- Geometry, Differential.

Choose an application

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

This book uses algebraic tools to study the elementary properties of classes of fields and related algorithmic problems. The first part covers foundational material on infinite Galois theory, profinite groups, algebraic function fields in one variable and plane curves. It provides complete and elementary proofs of the Chebotarev density theorem and the Riemann hypothesis for function fields, together with material on ultraproducts, decision procedures, the elementary theory of algebraically closed fields, undecidability and nonstandard model theory, including a nonstandard proof of Hilbert's irreducibility theorem. The focus then turns to the study of pseudo algebraically closed (PAC) fields, related structures and associated decidability and undecidability results. PAC fields (fields K with the property that every absolutely irreducible variety over K has a rational point) first arose in the elementary theory of finite fields and have deep connections with number theory. This fourth edition substantially extends, updates and clarifies the previous editions of this celebrated book, and includes a new chapter on Hilbertian subfields of Galois extensions. Almost every chapter concludes with a set of exercises and bibliographical notes. An appendix presents a selection of open research problems. Drawing from a wide literature at the interface of logic and arithmetic, this detailed and self-contained text can serve both as a textbook for graduate courses and as an invaluable reference for seasoned researchers.

Algebra. --- Mathematics. --- Algebraic geometry. --- Algebraic fields. --- Polynomials. --- Geometry. --- Mathematical logic. --- Algebraic Geometry. --- Field Theory and Polynomials. --- Mathematical Logic and Foundations. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Euclid's Elements --- Algebra --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebraic number theory --- Rings (Algebra) --- Mathematical analysis --- Math --- Science --- Algebraic geometry --- Geometry --- Cossos algebraics --- Teoria algebraica de nombres --- Geometry, Algebraic. --- Logic, Symbolic and mathematical.