There are eight units - (i) Numbers, Quantification and Numerical Applications, (ii) Algebra, (iii) Inferential Statistics, (iv) Index Numbers and Time-based data, (v) Calculus, (vi) Financial Mathematics, (vii) Linear Programming, and (viii) Probability.

### Course Structure

S.No. |
Unit |
Marks |

I | Numbers, Quantification and Numerical Applications | 6 |

II | Algebra | 10 |

III | Inferential Statistics | 6 |

IV | Index Numbers and Time-based data | 10 |

V | Calculus | 15 |

VI | Financial Mathematics | 15 |

VII | Linear Programming | 8 |

VIII | Probability | 5 |

Total |
80 |

### Unit I: Numbers, Quantification and Numerical Applications

- Modulo Arithmetic
- Congruence modulo
- Simple arithmetic functions
- Allegation or Mixture
- Numerical problems on boats and streams; partnership; pipes and cistern; races and games, scheduling
- Numerical inequalities

### Unit II: Algebra

- Solution of simultaneous linear equations using elimination method (up to 3 variables)
- Matrices and types of matrices
- Algebra of matrices
- Determinants
- Inverse of a matrix
- Cramer’s rule and its application
- Simple applications of matrices and determinants including Leontiff input output model for two variables

### Unit III: Calculus

- Application of derivatives
- Increasing/Decreasing functions
- Maxima and Minima
- Marginal cost and marginal revenue using derivatives
- Integration
- Indefinite integral as family of curves
- Definite integral as area under the curve
- Integration of simple algebraic functions (primitive, by substitution, by parts)
- Application of Integration (consumer surplus-producer surplus)
- Differential equation (definition, order, degree)
- Formulating and solving linear differential equation
- Application of differential equation (Growth and Decay Model)

### Unit IV: Probability

- Probability Distribution
- Mathematical Expectation
- Variance
- Binomial Distribution
- Poisson distribution
- Normal distribution
- Basic applications and inferences

### Unit V: Inferential Statistics

- Population and sample
- Parameter, statistic and statistical inferences
- t-Test (one sample t-test and two independent groups t-test)

### Unit VI: Index numbers and Time-based data

- Index numbers, uses of index numbers
- Construction of index numbers (simple and weighted)
- Tests of adequacy of index numbers (unit test and time reversal test)
- Time series, Time series analysis for univariant data sets
- Trend analysis by moving average method
- Trend analysis by fitting of linear trend line using least squares

### Unit VII: Financial Mathematics

- Perpetuity, Sinking funds
- Valuation of Bonds (Present value approach and Relative price approach)
- Calculation of EMI
- Calculation of returns, nominal rate of return, effective rate of interest
- Compound annual growth rate
- Stock, shares and debentures
- Linear method of depreciation

### Unit VIII: Linear Programming

- Introduction and related terminologies (constraints, objective function, optimization)
- Mathematical formulation of linear programming problems
- Different types of linear programming problems (Transportation and assignment problem)
- Graphical method of solution for problems in two variables
- Feasible and infeasible regions (bounded and unbounded)
- Feasible and infeasible solutions, optimal feasible solutions (up to three nontrivial constraints)