UPSC IFOS Mathematics Paper II Syllabus

UPSC IFOS Mathematics Paper II: topic-wise syllabus

1. 1

   Algebra

   Section A

   • Groups, subgroups and normal subgroups
   • Homomorphisms and isomorphism theorems
   • Sylow's theorems and permutation groups
   • Cayley's theorem
   • Rings, ideals and integral domains
   • Field extensions and finite fields
2. 2

   Real Analysis

   Section A

   • Real number system and completeness
   • Cauchy sequences
   • Continuity and uniform continuity
   • Riemann integral and improper integrals
   • Convergence of series
   • Uniform convergence of sequences and series of functions
   • Implicit function theorem and multiple integrals
3. 3

   Complex Analysis

   Section A

   • Analytic functions and Cauchy-Riemann equations
   • Cauchy's theorem and integral formula
   • Taylor and Laurent series
   • Singularities and residue theorem
   • Contour integration
   • Conformal and bilinear mappings
4. 4

   Linear Programming

   Section A

   • Basic feasible and optimal solutions
   • Graphical and simplex methods
   • Duality
   • Transportation and assignment problems
   • Travelling salesman problem
5. 5

   Partial Differential Equations

   Section B

   • Formulation of partial differential equations
   • Pfaffian differential equations
   • First order equations and Charpit's method
   • Cauchy's method of characteristics
   • Second order linear equations with constant coefficients
   • Vibrating string, heat and Laplace equations
6. 6

   Numerical Analysis and Computer Programming

   Section B

   • Bisection, Regula-Falsi and Newton-Raphson methods
   • Gaussian elimination, Gauss-Jordan and Gauss-Seidel methods
   • Newton's and Lagrange's interpolation
   • Simpson's, trapezoidal and Gaussian quadrature rules
   • Euler and Runge-Kutta methods
   • Binary, octal and hexadecimal systems
   • Bitwise and logical operations
   • Algorithms, flow charts and simple programs
7. 7

   Mechanics and Fluid Dynamics

   Section B

   • Generalised coordinates and constraints
   • D'Alembert's principle and Lagrange's equations
   • Hamilton's equations
   • Rigid body motion in two dimensions
   • Equation of continuity and Euler's equation
   • Potential flow, sources, sinks and vortices
   • Flow past a cylinder and sphere
   • Navier-Stokes equation