Mathematical Science Syllabus Paper 1 Section B Unit 1To 5
General Information: Units 1, 2, 3 and 4 are compulsory for all candidates. Candidates with Mathematics background may omit units 10-14 and units 17, 18. Candidates with Statistics background may omit units 6,7,9,15 and 16. Adequate alternatives would be given for candidates with O.R. Background.
1. Basic concepts of Real and Complex analysis: Sequences and series, continuity, uniform continuity, Differentiability, Mean Value Theorem, sequences and series of functions, uniform convergence, Riemann integral - definition and simple properties. Algebra of Complex numbers, Analytic functions, Cauchy's Theorem and integral formula, Power series, Taylor's and Laurent's series, Residues, Contour integration.
2. Basic Concepts of Linear Algebra: Space of n-vectors, Linear dependence, Basis, Linear transformation, Algebra of matrices, Rank of a matrix, Determinants, Linear equations, Quadratic forms. Characteristic roots and vectors.
3. Basic concepts of probability: Sample space, discrete probability, simple theorems on probability, independence of events, Bayes Theorem. Discrete and continuous random variables, Binomial, Poisson and
4. Linear Programming Basic Concepts: Convex sets. Linear Programming Problem (LPP). Examples of LPP. Hyperplane, open and closed half-spaces. Feasible, basic feasible and optimal solutions. Extreme point and graphical method.