TY - BOOK ID - 8434454 TI - Topics in physical mathematics PY - 2010 SN - 1447161211 1848829388 1848829396 1299337651 PB - London ; New York : Springer, DB - UniCat KW - Mathematical analysis. KW - Mathematical physics. KW - Mathematical physics KW - Mathematics KW - Engineering & Applied Sciences KW - Physical Sciences & Mathematics KW - Applied Physics KW - Geometry KW - Science KW - Mathematics. KW - Math KW - Algebra. KW - Field theory (Physics). KW - Global analysis (Mathematics). KW - Manifolds (Mathematics). KW - Differential geometry. KW - Topology. KW - Complex manifolds. KW - Differential Geometry. KW - Manifolds and Cell Complexes (incl. Diff.Topology). KW - Field Theory and Polynomials. KW - Global Analysis and Analysis on Manifolds. KW - Global differential geometry. KW - Cell aggregation KW - Global analysis. KW - Classical field theory KW - Continuum physics KW - Physics KW - Continuum mechanics KW - Analysis situs KW - Position analysis KW - Rubber-sheet geometry KW - Polyhedra KW - Set theory KW - Algebras, Linear KW - Aggregation, Cell KW - Cell patterning KW - Cell interaction KW - Microbial aggregation KW - Geometry, Differential KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Mathematical analysis KW - Analytic spaces KW - Manifolds (Mathematics) KW - Topology KW - Differential geometry UR - https://www.unicat.be/uniCat?func=search&query=sysid:8434454 AB - The roots of ’physical mathematics’ can be traced back to the very beginning of man's attempts to understand nature. Indeed, mathematics and physics were part of what was called natural philosophy. Rapid growth of the physical sciences, aided by technological progress and increasing abstraction in mathematical research, caused a separation of the sciences and mathematics in the 20th century. Physicists’ methods were often rejected by mathematicians as imprecise, and mathematicians’ approach to physical theories was not understood by the physicists. However, two fundamental physical theories, relativity and quantum theory, influenced new developments in geometry, functional analysis and group theory. The relation of Yang-Mills theory to the theory of connections in a fiber bundle discovered in the early 1980s has paid rich dividends to the geometric topology of low dimensional manifolds. Aimed at a wide audience, this self-contained book includes a detailed background from both mathematics and theoretical physics to enable a deeper understanding of the role that physical theories play in mathematics. Whilst the field continues to expand rapidly, it is not the intention of this book to cover its enormity. Instead, it seeks to lead the reader to their next point of exploration in this vast and exciting landscape. ER -