Author : Distinguished Professor Dr Letchmanan Naidu. ( Distinguished Professor of Pure and Applied Mathematical Sciences, Mathematical Physics, Mathematical Engineering, Mathematical Medicine, Mathematical Statistics and Mathematical Cosmology. ) Email : [email protected] Twitter : @profdr_rlnaidu (1) There are several main branches of mathematics, namely Pure Mathematics, Applied Mathematics, Computational Mathematics or Numerical Analysis, Discrete Mathematics, Mathematical Statistics including Probability Theory, Mathematical Logic and Mathematical Philosophy. Pure Mathematics is mainly abstract in nature and consists mainly of Set Theory, Real and Complex Analysis, Algebra ( Linear and Abstract Algebra), Geometry, Topology, Trigonometry, Ordinary and Partial Differential Equations, Functional Analysis, Advanced Calculus, etc. Pure Mathematics is extremely important and provides the essential mathematical methods and techniques required for solving scientific and technological problems in domains of applied mathematics. All students and research scholars in science and engineering, must make great effort to learn many topics in Pure Mathematics, as they are very useful for providing mathematical techniques, required for formulating solutions to complicated mathematical calculations. Many IVY League Universities have very strong assembly of prominent pure mathematicians, in the mathematics faculty. Many outstanding international awards in mathematics, like the Fields Medal, Clay Medal, Ramanujan Award, Bolyai Award, Hilbert Award, Cauchy Award and Banach Award, are normally awarded to Pure Mathematicians, who have made distinguished discovedries and outstanding contribution to development of mathematics.. (2) Applied Mathematics encompasses many fields of studies, such as Mathematical Physics, Mathematical Engineering, Mathematical Chemistry, Mathematical Biology, Mathematical Space Sciences ( Astronomy, Astrophysics, Relativity Theory and Cosmology ), Mathematical Theory of Chaos, Non-linear Dynamical Systems, Fractal Theory, Catastrophe Theory, Atmospheric Dynamics, Physical Oceanography & Ocean Dynamics, Fluid dynamics, Turbulence Theory and Vortex Dynamics, Galactic Dynamics, Magnetohydrodynamics, Electrodynamics and Mathematical Medicine, to name a few. Applied mathematics is also an exciting, challenging and fascinating field of study and research, as it enables us to apply the great mathematical techniques and methods of pure mathematics, to formulate mathematical models and pursue extensive calculations to analyse the physical, chemical, biological and environmental phenomena occurring both in nature and scientific laboratories, as well as, the design and analysis of engineering structures. (5) Mathematical Physics is also another very abstract field of study where rigorous pure mathematics techniques such as linear algebra, abstract algebra, vector analysis, tensor analysis, topology, knot theory, differential geometry, functional analysis, twistor theory, Hilbert Algebra, Dirac Algebra, Hecke Algebra, Lie Super-Algebra Grassmann Algebra, Clifford Algebra, Von-Neumann Algebra, Super-Manifold Theory, Riemanian Geometry and even C* Algebra has applications in Super-symmetry theory, Super-string Theory, Super-gravity theory, Quantum Mechanics, Relativistic Quantum Field Theory, Quantum Electrodynamics, Quantum Chromodynamics, Atomic Theory, Nuclear Theory, Elementary Particle Theory, General theory of Relativity, Relativistic Cosmology, Quantum Cosmology and Quantum Statistical Mechanics. Thus an excellent knowledge of advanced pure mathematics is very important for a mathematical physicist. Similarly areas of physical mathematics, such as integral transforms, integral equations, operational calculus, complex analysis, dyadics, special functions of mathematical physics, ordinary and partial differential equations of mathematical physics, approximation theory, perturbation theory, calculus of variation are very essential for performing calculations in theoretical mechanics, relativistic mechanics, quantum particle dynamics, fluid dynamics, electromagnetic theory, thermodynamics, aerodynamics, atmospheric dynamics, celestial mechanics and continuum mechanics, for the mathematical physicists to perform research calculations confidently and with elegance.
Posted on: Thu, 20 Nov 2014 09:04:23 +0000
Trending Topics
Recently Viewed Topics
© 2015