This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded in string theory. Secondly, this model is generalized to a web of dualities connecting topological string theory and N=2 supersymmetric gauge theories to a configuration of D-branes that intersect over a Riemann surface.
The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM.
Linear Operator Equations: Approximation and Regularization
Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.
The pedagogy used in Saxon Math is unique, effective, and research based. The authors of the Saxon Math series recognized that smaller pieces of information are easier to deliver and easier to learn. Rather than grouping topics into chapters, they separated complex concepts into increments and distributed them throughout each grade level. The result is a distributed approach in which instruction, practice, and assessment of concepts recur continually.
The pedagogy used in Saxon Math is unique, effective, and research based. The authors of the Saxon Math series recognized that smaller pieces of information are easier to deliver and easier to learn. Rather than grouping topics into chapters, they separated complex concepts into increments and distributed them throughout each grade level. The result is a distributed approach in which instruction, practice, and assessment of concepts recur continually.
