2025 Paper 2
- Q1a Cosets and Lagrange's theorem 10 marks
- Q1b Cyclic groups 10 marks
- Q1c Absolute and conditional convergence 10 marks
- Q1d Laurent's series in an annulus 10 marks
- Q1e LPP: standard form; basic, basic feasible, optimal solutions 10 marks
- Q2a Cauchy sequences; completeness of R 15 marks
- Q2b Euclidean domains 15 marks
- Q2c Contour integration of real integrals using residues 20 marks
- Q3a Residues: computation at poles of various orders 15 marks
- Q3b Lagrange's method of multipliers (constrained extrema) 20 marks
- Q3c Duality 15 marks
- Q4a Ring homomorphisms; quotient rings 15 marks
- Q4b Riemann integral 15 marks
- Q4c Transportation problem 20 marks
- Q5a Second-order linear PDEs with constant coefficients (CF, PI) 10 marks
- Q5b Gauss-Seidel iteration 10 marks
- Q5c-i Number systems 5 marks
- Q5c-ii Boolean algebra 5 marks
- Q5d Lagrange's equations 10 marks
- Q5e Sources, sinks, doublets 10 marks
- Q6a Laplace equation: Dirichlet/Neumann, separation of variables 20 marks
- Q6b Boolean algebra 15 marks
- Q6c Moment of inertia 15 marks
- Q7a Charpit's method 15 marks
- Q7b Lagrange's interpolation 15 marks
- Q7c Navier-Stokes equation for a viscous fluid 20 marks
- Q8a Cauchy's method of characteristics 15 marks
- Q8b Trapezoidal rule (composite; error) 15 marks
- Q8c-i Hamilton's equations 10 marks
- Q8c-ii Hamilton's equations 10 marks