# TU IOE MSc Entrance Syllabus for M.Sc. in Applied Mathematics (AM) Stream

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 consists 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%.

## Section-B

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

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