Course outcomes
M.A/M.Sc. (Mathematics)
Teaching Pattern for Semester I, II, III and IV

Four lectures per week per course. Each lecture is of 60 minutes duration.

In addition, there shall be tutorials, seminars as necessary for each of the five courses.
SemesterII
PSMT201 / PAMT201: ALGEBRA II
Course Outcomes:

Students will learn Dihedral groups, Matrix groups, Automorphism group, Inner
automorphisms, Structure theorem for nite abelain groups via examples.

Students will be able to understand group actions and orbitstabilizer formula;
Sylow theorems and applications to classication of groups of small order.

Students will be able to earn knowledge of prime avoidance theorem, Chinese remainder
theorem, and specialized rings like Euclidean domains, principal ideal domains,
unique factorization domains, their inclusions and counter examples.
PSMT202 / PAMT202: TOPOLOGY
Course Outcomes:

To understand a formation of new spaces from old one using product, box and
quotient topology.

This course create a building block for analysis as well as algebraic geometry.

Students will understand extension theorems (e.g. Tietze extension theorem) which
is useful in Functional Analysis.

This course covers the Tychonoff theorem which is a milestone of this subject.
PSMT 203/PAMT 203: ANALYSIS II
Course Outcomes:

In this course students are expected to understand the basic concepts of measure
on an arbitrary measure space X as well as on ℝ^{n}.

They are also expected to study Lebesgue outer measure of sets and measurable
sets, measurable functions.

Students will be able to understand the concepts of integrals of measurable functions
in an arbitrary measure space (X, A, μ). Lebesgue integration of complex valued
functions and basic concepts of signed measures.
PSMT 204 / PAMT 204 : PARTIAL DIFFERENTIAL EQUATIONS
Course Outcomes:

Students are expected to understand the basic concepts and method of nding the
solution of rst and second order Partial Differential Equations (PDEs).

Students will be able to know the classication of second order PDEs, singularity
and fundamental solution.

Students will be able to know the role of Green's function in the solution of Partial
Differential Equations.

Through this course students will understand existence and uniqueness of solutions
to Diffusion and Parabolic equations.
PSMT205 / PAMT205: PROBABILITY THEORY
Course Outcomes:

Students will understand the concept of Modelling Random Experiments, Classical
probability spaces, felds generated by a family of sets, feld of Borel sets, Limit
superior and limit inferior for a sequence of events.

Students will be able to know about probability measure, Continuity of probabilities,
First BorelCantelli lemma, Discussion of Lebesgue measure on eld of Borel
subsets of assuming its existence, Discussion of Lebesgue integral for nonnegative
Borel functions assuming its construction.

Students will be able to earn knowledge of discrete and absolutely continuous probability
measures, conditional probability, total probability formula, Bayes formula.

Students will learn distribution of a random variable, distribution function of a
random variable, Bernoulli, Binomial, Poisson and Normal distributions.

Students will be able to understand Chebyshev inequality, Weak law of large numbers,
Convergence of random variables, Kolmogorov strong law of large numbers,
Central limit theorem and Application of Probability Theory.