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.
PSMT101 /PAMT101: ALGEBRA I
Students will be able to understand the notion of dual space and double dual,
Annihilator of a subspace and its application to counting the dimension of a nite
dimensional vector space, Basics of determinants, applications to solving system of
equations, Nilpotent operators, invariant subspaces and its applications, Bilinear
forms and spectral theorem with examples of spectral resolution and Symmetric
bilinear form and Sylvester's law.
Students will be able to understand the applicability of the above concepts in different
courses of pure and applied mathematics and hence in other disciplins of
science and technology.
PSMT102 / PAMT102: ANALYSIS I
This course is the foundation course of mathematics, especially mathematical analysis.
Student will be able to grasp approximation of a differentiable function localized at
Inverse function theorem helps to achieve homeomorphism locally at a point whereas
implicit function theorem justies the graph of certain functions. Indirectly or
directly Unit III talks about value of a function in the neighbourhood of a known
In Unit IV, student will be able to understand the concept of Riemann integration.
PSMT103 / PAMT103: COMPLEX ANALYSIS
In this course the students will learn about series of functions and power series.
The concept of radius of convergence will be introduced and calculated.
This course gives insight of complex integration which is dierent from integration
of real valued functions. In particular, Cauchy integral formula will be proved.
The students will learn that if a function is once (complex) dieffrentiable then it is
innitely many times differentiable. This will be a sharp contrast with the theorems
of real analysis.
The various properties of obius transformations that have a wide variety of applications
along with major theorems of theoretical interest like Cauchy-Goursat
theorem, Morera's theorem, Rouche's theorem and Casorati-Weierstrass theorem
will be studied.
PSMT104 / PAMT104: ORDINARY DIFFERENTIAL EQUATIONS
Through this course students are expected to understand the basic concepts of
existence and uniqueness of solutions of Ordinary Differential Equations (ODEs).
In case of nonlinear ODEs, students will learn how to construct the sequence of approximate
solutions converges to the exact solution if exact solution is not possible.
Students will be able to understand the qualitative features of solutions.
Students will be able to identify Sturm Liouville problems and to understand the
special functions like Legendre's polynomials and Bessel's function.
Students will be to understand the applicability of the above concepts in dierent
disciplins of Techonolgy.
PSMT105 / PAMT105: DISCRETE MATHEMATICS
Students will solve Linear Diophantine equations, cubic equation by Cardano's
Method, Quadratic Congruence equation. Students will learn the multiplicativity
of function τ, σ and φ.
Students will be able to understand the proof of Erdos- Szekers theorem on monotone
sub-sequences of a sequence with n²+1 terms and the applicability of Forbidden
Stundent will learn the Fibonacci sequence, the Linear homogeneous recurrence relations
with constant coecient, Ordinary and Exponential generating Functions,
exponential generating function for bell numbers, the applications of generating
Functions to counting and use of generating functions for solving recurrence relations.
Stundents will be able to understand Polyas Theory of counting, Orbit stabilizer
theorem, Burnside Lemma and its applications, Applications of Polya's Formula.