The major constraint of this course is to understand the analytical and numerical techniques of computing solution of non-linear algebraic system of equations, non-linear equations, ordinary and partial differential equations. Moreover this also comprises of optimization theory, approximation theory, interpolation techniques and methods of computing quadrature. Mathematics software packages like Maple and Mat lab will be used throughout the course to obtain numerical results/simulations. 

Calculus-III or Calculus of several variables, applies the techniques and theory of differentiation and integration to vector-valued functions and functions of more than one variable. The course presents a thorough study of vectors in two and three dimensions, vector-valued functions, curves and surfaces, motion in two and three dimensions, and an introduction to vector fields. Students will be exposed to modern mathematical software to visually represent these 2D and 3D objects.

This one-semester three-credit course in Introductory Topology will have three general interconnected objectives.
First, as it has become increasingly apparent that topology is one of the major branches of modern mathematics, this course will provide a firm foundation in topology to enable the student to continue more advanced study in this area. Second, as several important areas of mathematics, in particular modern analysis, depend upon or are clarified by the certain topics in topology, this course will present and emphasize those topics in order to aid the student in his future mathematical studies. Finally, this course hopes to expose the students to both mathematical rigor and abstraction, giving there an opportunity further to develop his mathematical maturity.
 The key course contents are, topological spaces; separation axioms; continuity, convergence, connectedness, and compactness; basic notions in homotopy theory; quotient spaces; and paracompactness.

Much of mathematics relies on our ability to be able to solve equations, if not in explicit exact forms, then at least in being able to establish the existence of solutions. To do this requires a knowledge of so-called "analysis", which in many respects is just Calculus in very general settings. The foundations for this work are commenced in Real Analysis, a course that develops this basic material in a systematic and rigorous manner in the context of real-valued functions of a real variable. Topics covered are: Basic set theory. The real numbers and their basic properties. Sequences: convergence, sub-sequences, Cauchy sequences. Open, closed, and compact sets of real numbers. Continuous functions and uniform continuity. The Riemann integral. Differentiation and Mean Value theorems. The Fundamental Theorem of Calculus. Series. Power series and Taylor series. Convergence of sequences and series of functions.