Edusanjal

February 09, 2023

AM is the entrance stream for enrollment in the M.Sc in Applied Mathematics program.

The M.Sc. Entrance examination will be **“Computer Based Examination” **of two hours duration, consisting of two sections. **Section- A **consists of 45 questions for 50 marks. While **Section-B c**onsists of stream specialized course with 50 questions of 1 mark each. Each question will be of objective type with multiple choice answers and negative marking for each wrong answer is 10%.

**1. Calculus [15]**

• Double integral; First order linear and non- linear differential equations; Differential equation of first order and first degree and their applications; Linear differential equations with constant coefficients; Second order linear differential equations; Partial differential equation of first order

**2. Algebra [15]**

• Binary operations and properties of integers: Binary operations, algebraic structures, equivalence relations and equivalence classes, properties of integers and prime number, divisors and greatest common divisors, prime factors and unique factorization theorem, congruencies and residue classes.

• Groups : Definition, semi-groups and groups, order of a group, properties of groups, integral power of an element, subgroups and their properties, cyclic groups, order of an element of a group, normalizer, permutation groups, normal subgroups, quotient groups and their properties, homomorphism, kernel and isomorphism

• Rings and fields: Rings and their special classes, elementary properties of rings, zero divisor and division ring, integral domain, field and their properties.

• Theory of polynomial equations, cubic and biquadratic equations, numerical solution of equations

• Linear maps and matrices.

**3. Mathematical Analysis [10]**

• Elementary logic

• Real number system, point set topology of the real line, sequences and series of the real numbers

• Euclidian spaces and metric spaces, completeness, sequences in metric space, sequences and series of functions

• Improper integrals

**4. Fundamentals of Statistics [10]**

• Population and sample, Presentation of data

• Measures of central tendency and Measures of dispersion

• Moments, skewness and kurtosis

• Index numbers, Time series analysis

• Correlation and regression, Analysis of categorical data

• Estimation and hypothesis testing