2013 Paper 2
- Q1a Fields and finite fields 10 marks
- Q1b Cyclic groups 10 marks
- Q1c Riemann integral 10 marks
- Q1d Cauchy's residue theorem 10 marks
- Q1e Simplex method (basic) 10 marks
- Q2a Permutation Groups (S_n): Cycle Decomposition, Sign, A_n 10 marks
- Q2b Permutation Groups (S_n): Cycle Decomposition, Sign, A_n 13 marks
- Q2c Uniform convergence of series 13 marks
- Q2d Real number system as ordered field with LUB property 14 marks
- Q3a Euclidean domains 15 marks
- Q3b Ring homomorphisms; quotient rings 15 marks
- Q3c Maxima and minima of single-variable functions 10 marks
- Q3d Riemann integral 10 marks
- Q4a Assignment problem (Hungarian method) 15 marks
- Q4b Contour integration of real integrals using residues 15 marks
- Q4c Simplex method (basic) 20 marks
- Q5a Family of surfaces 10 marks
- Q5b Classification and reduction to canonical form 10 marks
- Q5c Newton's forward difference interpolation 10 marks
- Q5d Vortex motion; circulation 10 marks
- Q5e Moment of inertia 10 marks
- Q6a Second-order linear PDEs with constant coefficients (CF, PI) 15 marks
- Q6b Quasilinear first-order PDEs (Lagrange's method) 15 marks
- Q6c Wave equation 20 marks
- Q7a Newton-Raphson method (convergence, geometric meaning) 20 marks
- Q7b Euler's method (and modified Euler) 15 marks
- Q7c Simpson's 1/3 and 3/8 rules 15 marks
- Q8a Lagrange's equations 15 marks
- Q8b Sources, sinks, doublets 15 marks
- Q8c Vortex motion; circulation 20 marks