IAS Quesion of Mathematics >> Strategy Paper II
Paper II
Section A
Algebra: Normal subgroups, homomorphism of groups quotient groups basic isomorophism theorems, Sylow's group, principal ideal domains, unique factorisation domains and Euclidean domains. Field extensions, finite fields. Real Analysis: Riemann integral, improper integrals, absolute and conditional convergence of series of real and complex terms, rearrangement of series. Uniform convergence, continuity, differentiability and integrability for sequences and series of functions. Differentiation of functions of several variables, change in the order of partial derivatives, implicit function theorem, maxima and minima. Multiple integrals.
Complex Analysis: You can skip this entire section, if you have prepared other sections well.
Linear Programming: Basic solution, basic feasible solution and optimal solution, Simplex method of solutions. Duality. Transportation and assignment problems. Travelling salesman problems.
Section B
Partial differential equations: Solutions of equations of type dx/p=dy/q=dz/r; orthogonal trajectories, pfaffian differential equations; partial differential equations of the first order, solution by Cauchy's method of characteristics; Char-pit's method of solutions, linear partial differential equations of the second order with constant coefficients, equations of vibrating string, heat equation, laplace equation.Numerical Analysis and Computer programming: Numerical methods, Regula-Falsi and Newton-Raphson methods Numerical integration: Simpson's one-third rule, tranpesodial rule, Gaussian quardrature formula. Numerical solution of ordinary differential equations: Euler and Runge Kutta-methods.
Computer Programming: Binary system. Arithmetic and logical operations on numbers. Bitwise operations. Octal and Hexadecimal Systems. Convers-ion to and from decimal Systems.
Mechanics and Fluid Dynamics: D'Alembert's principle and Lagrange' equations, Hamilton equations, moment of intertia, motion of rigid bodies in two dimensions.
