1. Curriculum Aspects: The Department offers the following degrees

(i)      M.Sc. (Course Work)
(ii)      M.Phil(Course Work and initiation to Research)
(iii)     Ph.D.(Research)

The details are as follows,

M.Sc. Programme:

M.Sc. (Mathematics) is two year programme consisting of four semesters. The details of courses offered in each semester is as follows.

M.Sc. (Mathematics) Semester-I:(650 Marks)

Course work:

There will be 6 courses. The session work for each course will comprise of 3 lectures per week and one seminar per week. Each course will have a weighting of 100 marks (70 marks for University Examination + 30 marks for Internal Assessment. Internal Assessment will comprise of one internal test of 20 marks, a seminar of 5 marks and quizzes of 5 marks.). Each student will take 6 courses in consultation and with approval of the department.

List of Courses:

M. 401 Complex Analysis I

M. 402 Topology I

M. 403 Functions of Several Variables

M. 404 Linear Algebra

M. 405 Mechanics I

M. 406 Methods of Differential Equations

M. 407 Theory of Differential Equations

M.Sc. (Mathematics) Semester-II (650 Marks)

Course work:

There will be 6 courses. The session work for each course will comprise of 3 lectures per week and one seminar per week. Each course will have a weighting of 100 marks (70 marks for University Examination + 30 marks for Internal Assessment. Internal Assessment will comprise of one internal test of 20 marks, a seminar of 5 marks and quizzes of 5 marks.). Each student will take 6 courses in consultation and with approval of the department.

List of Courses:

M. 501 Real Analysis I

M. 502 Algebra I

M. 503 Differential Geometry

M. 504 Functional Analysis I

M. 505 Mechanics II

M. 506 Methods of Partial Differential Equations

M.Sc. (Mathematics) Semester-III (650 Marks)

Course work:

There will be 6 courses. The session work for each course will comprise of 3 lectures per week and one seminar per week. Each course will have a weighting of 100 marks (70 marks for University examination + 30 marks for internal assessment comprising of one internal test of 20 marks seminar of 5 marks and quizzes of 5 marks).

The courses are a classified into 3 groups:

Group A: Courses M. 601 to M. 610

Group B: Courses M. 611 to M. 617

Group C: Courses M. 617 to M. 623

Each student will take 6 courses as per the following scheme.

1.     Course M-601
2.     One course from group C
3.     Three  courses from group A or {two courses from group B and one   course from group A or group B or group C}.
4.   One course from group A or B or C.

A student shall choose the courses with the explicit approval of the Department and will be required to choose course from those offered by the Department.

Group-A

M-601 Real Analysis-II: Measure Theory

M-602 Functional Analysis II

M-603 Banach Algebras

M-604 Topology II

M-605 Differential Manifolds–I

M-606 Fourier Analysis–I

M-607 Wavelets

M-608 Group Theory

M-609 Algebraic Topology-I: Homotopy, Triangulations and Surfaces

M-610 Theory of Ordinary Differential Equations

M-611 Classical Riemannian Geometry

Group-B

M-611 Classical Riemannian Geometry

M-612 Relativity – I

M-613 Fluid Dynamics – I

M-614 Statistical Mechanics – I

M-615 Quantum Mechanics – I

M-616 Electromagnetic Theory – I

M-617 Mathematical Methods-I

Group-C

M-617 Mathematical Methods-I

M-618 Bio-Mathematics-I

M-619 Graph Theory – I

M-620 Operations Research

M-621 C++ programming and Mathematical algorithms –I

M-622 Problems and Exercises in Mathematics

M-623 Mathematical Modelling

M.Sc. (Mathematics) Semester-IV (650 Marks)

Course work:

There will be 6 courses. The session work for each course will comprise of 3 lectures per week and one seminar per week. Each course will have a weighting of 100 marks (70 marks for University examination + 30 marks for internal assessment comprising of one internal test of 20 marks seminar of 5 marks and quizzes of 5 marks).

The courses are a classified into 3 groups:

Group A: Courses M. 701 to M. 713

Group B: Courses M. 714 to M. 721

Group C: Courses M. 721 to M. 726

Each student will take 6 courses as per the following scheme.

1.      Course M-701

2.      One course from group C

3.      Three  courses from group A or {two courses from group B and one course from group A or group B or group C}.

4.      One course from group A or B or C.

A student shall choose the courses with the explicit approval of the Department and will be required to choose courses from those offered by the Department.

Group-A

M-701 Complex Analysis – II

M-702 Geometric Functional Analysis

M-703 Operator Theory

M-704 Algebra – II: Rings and Modules

M-705 Differential Manifolds – II

M-706 Fourier Analysis – II

M-707 Algebraic Topology – II: Homology, Degree Theory and Knots

M-708 Theory of Partial Differential Equations

M-709 Topological Groups

M-710 Disrtibutions and Sobolev Spaces

M-711 Ergodic Theory

M-712 Spectral Theory of Dynamical Systems

M-713 Compact Operators and Applications

Group-B

M-714 Relativity – II

M-715 Fluid Dynamics – II

M-716 Statistical Mechanics – II

M-717 Orbital Mechanics

M-718 Quantum Mechanics II

M-719 Classical Mechanics – III

M-720 Electromagnetic Theory – II

M-721 Mathematical Method – II

Group-C

M-721 Mathematical Methods – II

M-722 Graph Theory – II

M-723 Bio-Mathematics – II

M-724 C++ programming and Mathematical algorithms – II

M-725 Mathematics Education

M-726 Problems and Exercises in Mathematics

 M.Phil. Programme:

Course work:

A student has to take three courses. The sessional work for each course comprises of 3 lectures per week. Each course has a weighting of 100 marks. Every candidate opts for 3 courses from Courses Nos. M-1 to M-21. The choice of the course is subject to the approval of M.Phil. Committee. In addition to the course work, a Dissertation is to be prepared on a topic of advance level; the weighting of the dissertation is of 100 marks.

Courses of Studies:

M-1 : Operator theory-I
M-2 : Operator theory-II
M-3 : Functional analysis
M-4 : Analysis
M-5 : Topological algebras
M-6 : Topics in locally convex spaces
M-7 : Topics in von Neumann algebras
M-8 : Topics in C*-algebras
M-9 : Function algebras
M-10 : Topological groups and abelian harmonic analysis
M-11 : Fourier analysis
M-12 : Advanced complex analysis
M-13 : Unbounded operators in Hilbert spaces and semigroups
M-14 : Several real variables
M-15 : Problems and exercises in Mathematics
M-16 : Computer programming and Mathematical softwares
M-17 : Riemannian geometry and applications of differential forms in general relativity
M-18 : Advanced mechanics
M-19 : Fluid dynamics
M-20 : Electromagnetic theory
M-21 : General theory of relativity

2. Revision of Sylabii:
Normally courses are revised at the interval of three years and it takes one year to implement them. However the revision can be done at and when required subject to the approval of the University. Recently the revision was done w.e.f. 2004-2005 in order to introduce semester system.

3. Innovations in Teaching Programme:

• Specially Designed Optional Courses:
   Problems and Exercises in Mathematics. (For talented students preparing for a career in Higher Mathematics aiming at providing a training in problem solving Mathematics)
  
  Research Level Advanced Courses in
      Functional Analysis
      Banach Algebras and Operator Theory
      Operator Algebras
      Relativity and Cosmology
      Geometry

·         Computer Programming in C/C++

·         Use of Mathematical Software like Mathematica, MatLab and MACSYMA etc.

·         Mathematics Education (a course more of cultural nature than of vocational nature aimed at students preparing for a teaching career).

·         Courses on Mathematical Foundations of Theoretical Sciences like
    Classical Mechanics
     Relativity and Cosmology
     Quantum Mechanics
     Statistical Mechanics
     Fluid Dynamics

• Seminars by Students:
  As a part of M. Sc. Programme, every student has to give 6 seminars in a semester.
  A weekly seminar session is conducted for M.Phil. students where each  has to give seminars on advanced level topics.
  
• Practical Training on Computers:
  In the courses related with computer programming and computer software, the practicals are conducted using computers. Each students is given access to one computer for this purpose. A Computer Laboratory is established in the Department.

4.    Evaluation:
M.Sc.:

Each of six courses carries a weighting  of 100 marks comprising of 70 marks for External Examination by the University and 30 marks for internal assessment.

Internal Assessment:
Comprising of two internal tests of 20 marks, seminar of 5 marks and quizzes of 5 marks. Internal tests are conducted by the department and quizzes are conducted by the concerned teachers periodically along with the routine teaching work.

External Examination:
For each of the courses offered External the University conducts examination of 70 marks at the end of each semester. In each paper, there is a board appointed by the University consisting of an internal examiner and an external examiner.

Viva:
Besides separate examinations for each of the courses a Viva-Voce Examination of 50 marks is conducted by the University at the end of the semester covering all the courses offered during the semester. For this University appoints a board of examiners consisting of internal and external examiners.

M.Phil.:

Each of three courses carries a weighting of 100 marks comprising of 70 marks for External Examination by the University and 30 marks for internal assessment

Internal Assessment:
Comprising of two internal tests of 20 marks and seminar of 10 marks.

External Examination:
For each of the courses offered External the University conducts examination of 70 marks at the end of each academic year.

Dissertation:
A student is required to submit a dissertation on a topic of advance level under the supervision of a teacher. The dissertation carries 100 marks. It is evaluated by an external expert and the dissertation supervisor separately.

Viva:
A Viva-Voce Examination of 50 marks (25 marks for course work and 25 marks for dissertation work). The Viva-Voce Examination is conducted by the External Examiner of Dissertation, Dissertation Supervisor and the M.Phil. Committee.

5.Guest Lectures and Seminars:

During academic sessions the department organizes various guest lectures. Mathematicians from outside visits the department to deliver lectures on topics pertaining to teaching and research. The department also frequently organizes weekly departmental research seminars. As a supplement to formal class room teaching the department has instituted a new lecture series entitled “Something Extra” to inculcate mathematical culture and to train the students for mathematical exposition.