CBCGS [2017 - current]

CBGS [2013 - 2016]

Old [2000 - 2012]

## Topics with syllabus and resources

100.00 Complex Integration

- Complex Integration – Line Integral, Cauchy’s Integral theorem for simply connected regions, Cauchy’s Integral formula (without proof)
- Taylor’s and Laurent’s series (without proof)
- Zeros, poles of f(z), Residues, Cauchy’s Residue theorem
- Applications of Residue theorem to evaluate Integrals of the type

200.00 Matrices

- Eigen values and eigen vectors
- Cayley-Hamilton theorem (without proof)
- Similar matrices, diagonalisable of matrix
- Derogatory and non-derogatory matrices, functions of square matrix

300.00 Correlation

- Scattered diagrams, Karl Pearson’s coefficient of correlation, covariance, Spearman’s Rank correlation
- Regression Lines

400.00 Probability

- Baye’s Theorem
- Random Variables:- discrete & continuous random variables, expectation, Variance, Probability Density Function & Cumulative Density Function.
- Moments, Moment Generating Function.
- Probability distribution:- binomial distribution, Poisson & normal distribution. (For detail study)

500.00 Sampling Theory

- Test of Hypothesis, Level of significance, Critical region, One Tailed and two Tailed test, Test of significant for Large Samples:- Means of the samples and test of significant of means of two large samples.
- Test of significant of small samples:- Students t- distribution for dependent and independent samples.
- Chi square test:- Test of goodness of fit and independence of attributes, Contingency table.

600.00 Mathematical Programming

- Types of solution, Standard and Canonical form of LPP, Basic and feasible solutions, simplex method.
- Artificial variables, Big –M method (method of penalty).
- Duality, Dual simplex method.
- Non Linear Programming:- Problems with equality constrains and inequality constrains (No formulation, No Graphical method).