Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology.
Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory with the aim to provide newcomers to the field with solid foundations in topological K-theory.
The apparent contradiction of the results of the Fermi-Pasta-Ulam experiment conducted in 1953 and 1954 with the hypothesis that essentially any nonlinearity would lead to a system exhibiting ergodic behaviour has become known as the Fermi-Pasta-Ulam Problem.
From the reviews of the 2nd edition The substantial development effort of this text clearly shows through in this new edition with its clear writing, good organisation, comprehensive coverage of essential theory, and well-chosen applications.
In modern financial practice, asset prices are modelled by means of stochastic processes, and continuous-time stochastic calculus thus plays a central role in financial modelling.
Objectives and Audience In the past three decades, we have witnessed the phenomenal growth in the trading of financial derivatives and structured products in the financial markets around the globe and the surge in research on derivative pricing theory.
Homological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years.
The monograph contributes to Lech's inequality - a 30-year-old problem of commutative algebra, originating in the work of Serre and Nagata, that relates the Hilbert function of the total space of an algebraic or analytic deformation germ to the Hilbert function of the parameter space.
The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus.
The main goal of the CIME Summer School on "e;Algebraic Cycles and Hodge Theory"e; has been to gather the most active mathematicians in this area to make the point on the present state of the art.
This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists.
The Session was intended to give a broad survey of the mathematical problems arising in the chaotic transition of deterministic dynamical systems, both in classical and quantum mechanics.
These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc.
