CBCGS [2017 - current]

CBGS [2013 - 2016]

Old [2000 - 2012]

## Topics with syllabus and resources

100.00 Matrices

101.00 Brief Revision of Vectors Over a Real Field

- Brief revision of vectors over a real field, inner product, norm, Linear Dependance and Independence and orthogonality of vectors.

102.00 Characteristic Polynomial

- Characteristic polynomial,
- characteristic equation,
- characteristic roots and characteristic vectors of a square matrix,
- properties of characteristic roots and vectors of different types of matrices such as orthogonal matrix, Hermitian matrix, Skew-Hermitian matrix,
- Cayley Hamilton theorem ( without proof) Functions of a square matrix, Minimal polynomial and Derogatory matrix.

200.00 Vector Calculus

201.00 Brief Revision of Scalar and Vector Point Functions

- Brief revision of Scalar and vector point functions, Gradient, Divergence and curl.

202.00 Line Integrals, Surface Integrals, Volume Integrals

- Line integrals, Surface integrals, Volume integrals.
- Green’s theorem(without proof) for plane regions and properties of line integrals, Stokes theorem(without proof),
- Gauss divergence theorem (without proof) related identities and deductions.(No verification problems on Stoke’s Theorem and Gauss Divergence Theorem)

300.00 Non Linear Programming

301.00 Unconstrained Optimization

- Unconstrained optimization, problems with equality constraints Lagranges Multiplier method.

302.00 Problem with Inequality

Problem with inequality constraints Kuhn-Tucker conditions.

400.00 Probability Distributions

401.00 Discrete and Continuous Random Variables

- Discrete and Continuous random variables, Probability mass and density function,
- Probability distribution for random variables, Expected value, Variance.

402.00 Probability Distributions

- Binomial, Poisson and Normal Distributions. For detailed study.

500.00 Sampling Theory

501.00 Sampling Distribution

- Sampling distribution. Test of Hypothesis. Level of significance, critical region.
- One tailed and two tailed tests. Interval Estimation of population parameters.
- Large and small samples.

502.00 Test of Significance for Large Samples

- Test of significance for Large samples: Test for significance of the difference between sample mean and population means,
- Test for significance of the difference between the means of two samples.

503.00 Studentâ€™S T-distribution

- Student’s t-distribution and its properties.
- Test of significance of small samples: Test for significance of the difference between sample mean and population means,
- Test for significance of the difference between the means of two Samples, paired t-test.

504.00 Analysis of Variance(F-test)

- One way classification, Two-way classification(short-cut method)

505.00 Chi-square Distribution

- Chi-square distribution and its properties, Test of the Goodness of fit and Yate’s correction

600.00 Correlation and Regression

601.00 Correlation, Co-variance

- Correlation, Co-variance, Karl Pearson Coefficient of Correlation & Spearman’s Rank Correlation Coefficient (non-repeated & repeated ranks )

602.00 Regression Coefficients

- Regression Coefficients & lines of regression