Sl. No. 
Name of the Paper 
Course Outcomes 
After the completion of the course, the students will be able: 
1 
Foundations of Mathematics 
 To explain the concepts of mathematical logic methods.
 To illustrate the idea of sets, set operations and functions.
 To analyze the properties of relations.
 To solve polynomial equations using numerical methods.

2 
Analytic Geometry , Trigonometry and Differential Calculus 
 To interpret the ideas of conic sections, tangents and normal to a conic and their properties.
 To determine the parametric forms of conic sections.
 To apply the concepts of trigonometric functions, their properties and summation of trigonometric series.
 To solve problems involving successive differentiation and indeterminate forms.

3 
Calculus 
 To determine the Taylor and Maclaurin series expansions of given functions.
 To compute curvature and related parameters of a given curve or curves.
 To calculate the partial derivatives, maxima and minima of functions and Lagrange multipliers for extremum problems.
 To solve the area and volume problems using multiple integrals.

4 
Vector Calculus, Theory of Numbers and Laplace transform 
 To determine the arc length, unit tangent vector, unit normal vector, gradient vector and directional derivatives of vector functions.
 To examine the applications of vector integration.
 To apply the concept of congruence, Fermat’s theorem, Wilson’s theorem and Euler’s phi function.
 To determine the Laplace transform of a given function.

5 
Mathematical Analysis 
 To use the ideas of finite and infinite sets and the properties of set of real numbers.
 To explain the idea of sequences and their convergence.
 To detect the convergence and divergence of sequences.
 To interpret the concepts of series, alternating series their convergence and absolute convergence.
 To solve problems involving the convergence and absolute convergence of series.
 To apply the concept of limit of functions.

6 
Differential Equations 
 To explain the concepts of nature of solutions of differential equations, exact equations and homogeneous equations
 To solve second order linear differential equations using different methods.
 To compute the solutions of second order linear differential equations using power series method.
 To determine the solutions of first order partial differential equations.

7 
Abstract Algebra 
 To explain the concepts of binary structures, groups and subgroups.
 To demonstrate different finite group structures using permutation groups.
 To analyse the concepts of homomorphism of groups and factor groups using theorems and examples.
 To illustrate the idea of normal subgroups through theorems.
 To categorize different binary structures into groups, rings, integral domains and fields.
 To deduce the concepts of ideals and factor rings from the concepts of normal subgroups and factor groups.

8 
Human Right and Mathematics for Environmental Studies 
 To discuss the basic knowledge about environment.
 To explain different kinds of environmental pollution and its causes.
 To identify the need of environmental protection.
 To apply knowledge about Fibonacci numbers.
 To estimate the value of Golden ratio.
 To describe various rules protecting human rights.
 To explain various bodies of UNO constituted for the protection of human rights.

9 
Open CourseApplicable Mathematics 
 To develop mathematical skills.
 To apply shortcut methods for solving problems.
 To explain the basic operations in Mathematics.
 To describe the definitions of trigonometric ratios.
 To acquire the basic arithmetic skills involving percentage, average, time and distance and elementary algebra.

10 
Real Analysis 
 To explain continuity and discontinuity of various functions.
 To explain the meaning of derivative of a function.
 To describe theorems associated with differentiability.
 To acquire knowledge about L’ Hospital rule and limits.
 To acquire the idea about Riemann integrability and Riemann integration.
 To explain uniform convergence of a series.
 Distinguish between pointwise convergence and uniform convergence.

11 
Graph Theory and Metric Spaces 
 To explain basic concepts of graphs, directed graphs and weighted graphs.
 To describe the properties of trees, spanning trees, cut vertices and connectivity.
 To examine Eulerian and Hamiltonian graphs.
 To explain the basic concepts of metric spaces.
 To discuss open sets, closed sets and Cantor set.
 To establish the concepts of convergence, completeness and continuous mapping in metric spaces.

12 
Complex Analysis 
 To explain the concepts of limit, continuity of complex functions and analytic functions.
 To use elementary complex functions.
 To integrate
 To examine the convergence of complex sequence and series.
 To detect singular points and residues.
 To evaluate improper integrals.

13 
Linear Algebra 
 To deduce the given matrix using the process of Gaussian elimination.
 To compute the rank of a matrix.
 To explain the concepts of vector spaces and subspaces.
 To detect linear independent sets and basis.
 To explain linear mapping and linear transformation.
 To find kernel and range of a transformation.
 To explain theorems associated with linear transformations.
 To compute eigen values and eigen vectors of transformation.

14 
Choice Based Operations Research 
 To translate the real world problems into corresponding linear programming problem.
 To apply the concepts of duality in solving linear programming problem.
 To solve transportation and assignment problems.
 To describe the concept of Game theory.

15 
Project 
 To demonstrate their own work.
 To produce a mature oral presentation of a non trivial mathematical topic.
 To investigate their awareness in relation to the wider research field.

16 
Partial Differentiation, Matrices, Trigonometry and Numerical Methods. 
 To draw graphs, level curves and contours.
 To discuss about partial derivatives.
 To practice questions to find the rank of a matrix using elementary transformations and solve linear equations.
 To apply CayleyHamilton theorem.
 To discuss about hyperbolic and circular functions.
 To compute summation of infinite series.
 To use numerical methods to find solutions of algebraic and transcendental equations.

17 
Integral Calculus and Differential Equations 
 To apply definite integrals to find volumes, length of plane curves and area of surfaces of revolution.
 To use multiple integrals to find volume of a solid and area of bounded regions.
 To discuss about first order ordinary differential equations and partial differential equations.
 To solve first order differential equation and partial differential equation.

18 
Vector Calculus, Analytic Geometry and Abstract Algebra 
 To solve problems involving vector valued functions
 To use Green’s theorem, Stoke’s theorem to integrate in vector fields.
 To illustrate the idea about conic sections, polar coordinates and conics in polar coordinates.
 To discuss about groups, cyclic groups and homomorphism of groups.

19 
Fourier Series, Laplace Transform and Complex Analysis 
 To discuss about periodic functions, trigonometric series and Fourier series.
 To solve differential equations using power series method.
 To explain Laplace transforms.
 To apply Laplace transforms to solve differential equations.
 To discuss about complex numbers and analytic functions.
 To use CauchyRiemann equations to
 To implement Cauchy integral theorem for complex integration.
