Course Code

MAT101

Course Title

Elementary Algebra

Course Outcomes

On the completion of the course the student will be able to

CO1: Understand De Moivre’s theorem and its applications

CO2: Understand properties of congruence and Fundamental theorem of Arithmetic

CO3: Discuss the matrices, row and column rank, echelon form, normal form, solution of system of linear equations

CO4: Determine eigenvalues and corresponding eigenvectors for a square matrix and application of Cayley Hamilton Theorem

Course Code

MAT102

Course Title

Calculus

Course Outcomes

On the completion of the course the student will be able to

CO1: Understand concept of limits, continuity and differentiability. 

CO2: Employ the concepts of asymptotes, and inflexion points in tracing of cartesian curves.

CO3: Evaluate integrals and its application to find arc length and area under curve.

CO4: Understand continuity and differentiability in terms of limits of vector valued functions.

Course Code

MAT103

Course Title

Basics of MATLAB

Course Outcomes

On the completion of the course the student will be able to

CO1: Make use of arrays in MATLAB

CO2: Do 2D plotting in MATLAB

CO3: Do 3D plotting in MATLAB

CO4: Understand multiple and parametric plots of 2D and 3D

Course Code

MAT111

Course Title

Theory of Equations

Course Outcomes

On the completion of the course the student will be able to

CO1: Learn general properties of polynomials and equations, nature of roots of an equation and relation between roots and coefficients.

CO2: Solve the reciprocal equations.  Transform the equation according to various given conditions and to.

CO3: To solve cubic and biquadratic equations Find the sum of the power of the roots of an equation using Newton’s Method.

CO4: Location and nature of roots by Sturm’s method. Condition for an equation to have real roots. Obtain integral and real roots of an equation.

Course Code

MAT112

Course Title

Ordinary Differential Equations

Course Outcomes

On the completion of the course the student will be able to

CO1: Understand basic concepts of differential equations and learn different methods to solve them.

CO2: To find solution differential equations using various methods.

CO3: Discuss the solution of second order differential equations using various techniques.

CO4: Form the models of real-life applications using differential equation.

Course Code

MAT201

Course Title

Partial Differential Equations

Course Outcomes

On the completion of the course the student will be able to

CO1: Observe basic concepts of partial differential equations related to degree, order with its classification as linear and nonlinear.

CO2: Discuss the solution of first and second order partial differential equations using various techniques.

CO3: Describe model of physical phenomena using partial differential equations such as the heat, wave and Laplace equations.

CO4: Analyze the fundamental and elementary solutions of boundary value problems.

Course Code

MAT202

Course Title

Analytical Geometry

Course Outcomes

On the completion of the course the student will be able to

CO1: Understand concept of pair of straight lines and circles.

CO2: Understand fundamental concepts and properties of conics.

CO3: Understand fundamental concepts of sphere and cone.

CO4: Understand fundamental concepts of cylinders and conicoids.

Course Code

MAT211

Course Title

Group Theory-I

Course Outcomes

On the completion of the course the student will be able to

CO1: To recognize the mathematical objects called groups.

CO2: To understand the concept of Cyclic Groups and to learn cyclic notation for permutations and its types.

CO3: To explain the significance of the notions of cosets, normal subgroups, and factor groups and to learn Lagrange’s theorem and its consequences.

CO4: Describe about structure preserving maps between groups and their consequences.

Course Code

MAT212

Course Title

Elementary Real Analysis

Course Outcomes

On the completion of the course the student will be able to

CO1: Demonstrate competence with the algebraic and order properties of real numbers.

CO2: Demonstrate competence with open and closed sets.

CO3: Demonstrate competence with elementary properties of sequences.

CO4: Demonstrate competence with the convergence and divergence of series.

Course Code

MAT213

Course Title

Numerical Analysis

Course Outcomes

On the completion of the course the student will be able to

CO1: understand the methods to solve algebraic as well as transcendental equations and do the programming related to these methods.

CO2: Learn relations between different operators and interpolation and do the programming related to these methods.

CO3: Learn numerical integration and do the programming related to these methods.

CO4: Learn solution of ordinary differential equation do the programming related to these methods.

Course Code

MAT301

Course Title

Theory of Real Functions

Course Outcomes

On the completion of the course the student will be able to

CO1: Demonstrate competence with the limits and continuity of real functions.

CO2: Demonstrate competence with differentiation of real functions.

CO3: Demonstrate competence with mean value theorems and their applications.

CO4: Demonstrate competence with Taylor’s theorem and its applications.

Course Code

MAT302

Course Title

Group theory II

Course Outcomes

On the completion of the course the student will be able to

CO1: Understand Automorphism group in both finite and infinite cyclic groups and characteristics subgroup

CO2: Understand directs product of groups and fundamental theorem of finite abelian groups

CO3: Understand group actions, related notion and application of group actions

CO4: Understand the fundamental concepts of Sylow p-subgroups, Sylow theorems

Course Code

MAT303

Course Title

Probability Theory

Course Outcomes

On the completion of the course the student will be able to

CO1: Understand types of data and their attributes, representation of data.

CO2: Understand Measures of Central tendency and Measures of Dispersion.

CO3: Understand Probability, Random variables, Correlation and Regression.

CO4: Understand Probability Distribution, t-test, Chi-Square test, F-test.

Course Code

MAT311

Course Title

Riemann Integration and series of functions

Course Outcomes

On the completion of the course the student will be able to

CO1: Demonstrate competence with the concept of Riemann Integration.

CO2: Demonstrate competence with the properties and applications of Riemann Integration.

CO3: Demonstrate competence with the concept of Uniform Convergence.

CO4: Demonstrate competence with the concept of Power Series.

Course Code

MAT312

Course Title

Multivariate Calculus

Course Outcomes

On the completion of the course the student will be able to

CO1: Understand basic concepts of limits, continuity, partial derivatives and applications of multivariate functions.

CO2: Get in depth knowledge of techniques for evaluation of extreme value of multivariate functions

CO3: Learn various applications of double and triple integrals.

CO4: Understand basics of vector calculus and its applications in interdisciplinary fields.

Course Code

MAT313

Course Title

Ring Theory and Linear Algebra

Course Outcomes

On the completion of the course the student will be able to

CO1: To describe the fundamental concepts in ring theory such as ideals, quotient rings, integral domains, and fields.

CO2: To learn structure preserving maps between rings and their properties.

CO3: To demonstrate the concepts of vector spaces, subspaces, bases, dimension and their properties with examples.

CO4: To identify matrices with linear transformations and the change of coordinate matrix and be able to find the domain, range, kernel, rank, and nullity of a linear transformation.

Course Code

MAT314

Course Title

Mechanics

Course Outcomes

On the completion of the course the student will be able to

CO1: Understand the concepts of equilibrium in case of number of coplanar concurrent forces and basic notions of parallel forces.

CO2: Understand basic concepts of Moment and couple.

CO3: Understand the applications of Newton laws of motion and basic concepts of SHM

CO4: Understand the fundamental concepts related to curvilinear motion and principles of work and energy.

Course Code

MAT401

Course Title

Abstract Algebra

Course Outcomes

On the completion of the course the student will be able to

CO1: Learn the applications of Sylow Theorems and different tests to check simplicity of groups.

CO2: Characterize all finite and finitely generated abelian groups.

CO3: Understand the subnormal and normal series for the solvable groups.

CO4: Understand different types of ideals and connection between ideal of a ring and matrix ring over it.

Course Code

MAT402

Course Title

Mathematical Statistics

Course Outcomes

On the completion of the course the student will be able to

CO1: Learn Probability distributions.

CO2: Learn Sampling Theory and Hypothesis testing.

CO3: Learn Hypothesis Testing.

CO4: Learn Large Sample tests.

Course Code

MAT403

Course Title

Metric Spaces

Course Outcomes

On the completion of the course the student will be able to

CO1: Learn Basic set topology and Sequences and series and their convergence

CO2: Understand the basic concepts of Metric spaces and their completeness

CO3: Understand the concepts of continuity in metric spaces.

CO4: Theorems on boundedness, Uniform continuity and theorems on various properties of Metric space.

Course Code

MAT404

Course Title

Number Theory

Course Outcomes

On the completion of the course the student will be able to

CO1: Learn Division Algorithm, Congruences and reduced residue system.

CO2: Learn Chinese Remainder theorem, Euler’s theorem and Arithmetic functions.

CO3: Learn Quadratic residues and Quadratic reciprocity law.

CO4: Learn Diophantine Linear Equations and Continued fractions.

Course Code

MAT405

Course Title

Complex Analysis

Course Outcomes

On the completion of the course the student will be able to

CO1: Learn about functions of complex variables and their Analyticity.

CO2: Learn about Complex Integration.

CO3: Learn about zeros and singularities of complex functions.

CO4: Learn to calculate improper integrals.

Course Code

MAT411

Course Title

Advanced Linear Algebra

Course Outcomes

On the completion of the course the student will be able to

CO1: Learn about linear transformations and its association with matrices.

CO2: Learn about linear functionals and dual spaces.

CO3: Learn about Characteristic Values and Characteristic Vectors.

CO4: Learn about Inner Product Spaces and their Properties.

Course Code

MAT412

Course Title

Riemann Stieltjes Integration and Functions of Several Variables

Course Outcomes

On the completion of the course the student will be able to

CO1: Review of Riemann Integration, Introduction to Riemann Stieltjes Integration.

CO2: Understand Properties of the Riemann-Stieltjes integral and its applications.

CO3: Understand Uniform convergence & Equicontinuous families of functions.

CO4: Understand Functions of several variables and its differentiation.

Course Code

MAT413

Course Title

Differential geometry

Course Outcomes

On the completion of the course the student will be able to

CO1: Understand differential geometry of plane curves and space curves

CO2: Understand the orientability of surfaces

CO3: Understand geometrical interpretation of fundamental forms and principal curvature

CO4: Understand geodesic curves and related notions

Course Code

MAT414

Course Title

Mathematical Methods

Course Outcomes

On the completion of the course the student will be able to

CO1: Understand Functional and its properties, Brachistochrone problem, Geodesics.

CO2: Understand Variational problems for functionals involving several dependent variables, Approximate solutions of Boundary Value Problem- Rayleigh-Ritz method.

CO3: Understand Laplace Transforms and its properties and how to use it to solve differential equations.

CO4: Fourier series and Fourier transforms and its application.

Course Code

MAT415

Course Title

Discrete Mathematics

Course Outcomes

On the completion of the course the student will be able to

CO1: Learn the fundamentals of logics, truth tables, quantifiers and counting techniques.

CO2: Learn Pigeonhole principle, solution of recurrence relations and generating    functions.

CO3: Learn graph theory, Handshaking theorem, Planar and Non-planar graph.

CO4: Learn Boolean Algebra, Logic Gates and Lattice theory.

Course Code

MTH549

Course Title

Mathematical Methods

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand Functional and its properties, Brachistochrone problem, Geodesics.

CO2: Understand Variational problems for functionals involving several dependent variables, Approximate solutions of Boundary Value Problem- Rayleigh-Ritz method.

CO3: Understand Laplace Transforms and its properties and how to use it to solve differential equations

CO4: Fourier series and Fourier transforms and its application.

Course Code

MTH550

Course Title

Real Analysis

Course Outcomes

After successfully completing this course, the students will be able to

CO1: The concept of convergence of sequences, completion of metric space, countable and uncountable sets, compact sets.

CO2: The concept of continuous functions in metric space, uniform convergence of sequence of functions, uniform convergence and differentiation, uniform convergence and integration and uniform convergence and continuity.

CO3: Reimann-Stieltjes integral as a generalization of Reimann integral, and rectifiable curves.

CO4: Calculus of severable variables, differentiation of vector-valued functions of several variables, and the implicit function theorem.

Course Code

MTH558

Course Title

Differential Geometry

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand differential geometry of plane curves and space curves.

CO2:  Understand the orientability of surfaces.

CO3:  Understand geometrical interpretation of first fundamental form, second fundamental form and principal Curvature.

CO4: Understand geodesic curves and related notions.

Course Code

MTH553

Course Title

Linear Algebra

Course Outcomes

After successfully completing this course, the students will be able to

CO1: understand the concepts of range space and null space, their dimension and applications.

CO2: associate a matrix with a linear transformation, about characteristic and minimal polynomials, and characteristic vectors.

CO3: convert matrices in to their canonical forms such as diagonal form, triangular form and also will learn about linear functional and dual spaces.

CO4: learn about inner product spaces, orthogonal/orthonormal vectors and adjoint operators. 

Course Code

MTH555

Course Title

Complex Analysis

Course Outcomes

After successfully completing this course, the students will be able to

CO1:  Know the fundamental concepts of complex numbers.

CO2: Evaluate limits and checking the continuity of complex function & apply the concept of analyticity and the Cauchy-Riemann equations.

CO3: Evaluate complex integrals and apply Cauchy integral theorem and formula.

CO4: Solve the problems using complex analysis techniques applied to different situations in engineering and other mathematical contexts.

Course Code

MTH556A

Course Title

Theory of Measure and Integration

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand -algebras, measurable sets, measures, outer measure, Lebesgue measure, measurable functions.

CO2: Understand Lebesgue integral, difference between Riemann and lebesgue integrals, Convergence in measure.

CO3: Understand differentiation of monotone functions, functions of bounded variation, Lebesgue differentiation theorem, convex functions.

CO4: Understand L^p Spaces, convergence, completeness and approximations in L^p Spaces.

Course Code

MTH557A

Course Title

Mathematical Statistics

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand the concept of mathematical expectation, variance and moment generating function.

CO2: Acquire knowledge of discrete probability distribution and continuous probability distribution with their properties.

CO3: Understand types of sampling and various exact sampling distribution.

CO4: Understand MP and UMP test and likelihood ratio test.

Course Code

MTH552

Course Title

Algebra-I

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Illustrate the dihedral groups, symmetric groups, cyclic groups and analyze the applications of Lagrange's theorem.

CO2: Understand the fundamental illustrate the dihedral groups, symmetric groups, cyclic groups and analyze the applications of Lagrange's theorem.

CO3: Concepts of Sylow p-subgroups, Sylow theorems and their application in non-simplicity of groups.

CO4: Connect the fundamental concepts of rings, subrings and ideals.

Course Code

MTH562A

Course Title

Numerical Analysis

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Find the solution of algebraic as well as transcendental equations using various methods.

CO2: Do Interpolation using various methods.

CO3: Find the solution of system of equations, eigen values & eigen vectors, Curve fitting.

CO4: Do Numerical integration and able to find solution of differential equations.

Course Code

MTH563A

Course Title

Numerical Analysis Lab

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Write algorithms for numerical methods implementations.

CO2: Utilize a variety of numerical methods to find roots of an equation.

CO3: Able to program Interpolation, numerical differentiation and integration, solution of linear equations in MATLAB.

CO4: Able to solve initial-value problems of differential equation using different numerical methods in MATLAB.

Course Code

MTH661

Course Title

Topology

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand the definition of topology, subspace topology, product topology and concept of continuous functions.

CO2: Differentiate between connected spaces and path connected spaces

CO3: Understand compactness, Local compactness, basic notions of T2.

CO4: Understand normal spaces and regular spaces and related important theorems like Tietze Extension Theorem.

Course Code

MTH662

Course Title

Algebra-II

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand the concepts of Polynomial rings, UFD, PID, ED and relation between them.

CO2: Learn different criterions to check irreducibility of a polynomial, Concept of algebraic element, transcendental elements, Field extension, degree of extension and finite extensions.

CO3: Various field extensions, e.g. splitting fields, algebraically closed fields, normal extensions.

CO4: Concept of Galois groups and Galois extensions. Separable and inseparable extensions, Perfect Fields.

Course Code

MTH663

Course Title

Ordinary Differential Equations

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Explain the concept of differential equations and existence-uniqueness theorem of differential equations.

CO2: Solve systems of linear differential equations and determine fundamental solutions and independence using the Wronskian.

CO3: Understand the Strum Liouville problems and the ortho -normalization of functions.

CO4: Find solution of ordinary differential equations in more than three variables and understand the concept of singular points in differential equations.

Course Code

MTH660

Course Title

Integral Equations-I

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Basic concepts of integral equations and their classifications and their applications in solving ordinary differential equations and boundary value problems.

CO2: Introduction to Fredholm integral equations, The variational iteration method, The direct computation method, The successive approximations method, The method of successive substitutions, comparison between alternative methods and solution of Fredholm Integral Equations of second kind with separable kernel.

CO3: Introduction to Volterra’s integral equations, The Adomian decomposition method, the modified decomposition method, the variational iteration method, the series solution method, and conversion of Volterra equation to initial value problem, Successive approximations method, The method of successive substitutions, and their comparison.

CO4: Understand Volterra integral equations of the first kind, the series solution method, Conversion of first kind to second kind, Resolvent kernel and Volterra Integral Equation, working rule for evaluating the resolvent kernel and solution of Fredholm Integral Equation of second kind using Fredholm’s first theorem, Fredholm’s second fundamental theorem.

Course Code

MTH664

Course Title

Operation Research-I

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand the key concepts of Operational Research and Linear Programming and their role in various organizations.

CO2: Formulate real-world problems as a linear programming model and describe the theoretical workings of the graphical and simplex method, demonstrate the solution process by hand and solver.

CO3: Employ the suitable methods for improving transportation cost of transportation problems.

CO4: Solve integer programming problem with different techniques.

Course Code

MTH665

Course Title

Fluid Mechanics-I

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Determine equation of continuity, incompressible fluid flow, acceleration of fluid, conditions at a rigid boundary.

CO2: Apply the Euler’s equation of motion, Bernoulli’s equation and understand Kelvin’s theorem of circulation, equation of vorticity.

CO3: Understand sources, sinks and doublets, images in rigid planes, images in solid spheres, Stoke’s stream function.

CO4: Understand complex velocity potential, Milne Thomson circle theorem and applications, theorem of Blasius, Vortex rows, Karman Vortex Street.

Course Code

MTH678

Course Title

Advance Complex Analysis

Course Outcomes

After successfully completing this course, the students will be able to

CO1:  Learn about Harmonic functions and their properties.

CO2:  Learn about analytic continuation, open mapping theorem and Riemann mapping theorem.

CO3:  Understand Weirestrass elliptic functions and their applications.

CO4:  Understand Weirestrass Zeta functions and their applications.

Course Code

MTH679

Course Title

Module Theory and Galois Theory

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand the difference between modules and vector spaces and learn various types of modules.

CO2: Find the Smith Normal form and rational canonical forms over PID.

CO3: Check the chain conditions on modules and find the nil & Jacobson radical.

CO4: Apply Galois theory to solvability of polynomials by radicals.

Course Code

MTH667

Course Title

Functional Analysis

Course Outcomes

After successfully completing this course, the students will be able to

CO1: The concept of normed linear space, Banach space, and compactness of normed linear spaces.

CO2: The concept of linear operators and their properties, linear functionals and their properties, and dual and reflexive spaces, and their properties.

CO3: The concept of inner product spaces, Hilbert space, and its properties, projection theorem, orthonormal sets, etc.

CO4: Fundamental theorems for normed and Banach space, partially ordered set, adjoint operators, strong and weak convergence, and contraction theorem.

Course Code

MTH668

Course Title

Number Theory

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Learn Division Algorithm, Congruences and reduced residue system.

CO2: Learn Chinese Remainder theorem, Euler’s theorem and Arithmetic functions

CO3: Learn Quadratic residues and twin primes and Fermat’s numbers.

CO4: Learn Diophantine Linear Equations and Continued fractions.

Course Code

MTH675

Course Title

Classical Mechanics

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand the Lagrangian formulation and Lagrange’s dynamical equations of motion

CO2: Understand the Hamiltonian formulation and Hamiltonian’s dynamical equations of motion

CO3: Understand fundamental concepts of canonical transformation, invariance of Poisson bracket and Lagrange bracket.

CO4: Understand H-J equation, rigid body dynamical equations and Euler’s angles.

Course Code

MTH677

Course Title

Partial Differential Equations

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Describe theoretical aspects to solve linear and non-linear partial differential equations.

CO2: Enumerate methods for solving second order and higher order partial differential equations.

CO3: Describe model of physical phenomena using partial differential equations such as the heat equation, wave equation and Laplace equation.

CO4: Analyze the fundamental solutions and applications of heat equation, wave equation and Laplace equation.

Course Code

MTH666A

Course Title

Discrete Mathematics

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Learn Quantifiers, Logical statements and basic counting principle.

CO2: Learn Pigeon hole principle, Generating functions and solutions of recurrence relations.

CO3: Learn Different types of graph and coloring of graphs, solutions of problem related to graph and tree.

CO4: Learn boolean Algebra and its properties, Lattice and its Properties.

Course Code

MTH671

Course Title

Operation Research-II

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand the mathematical tools that are needed to solve inventory problems.

CO2: Conceptualise optimum event management through Network scheduling.

CO3: Analyze the queueing and its different models.

CO4: Understand methods like convex simplex method and penalty function methods for solving different types of nonlinear programming problems and Karush−Kuhn−Tucker conditions.

Course Code

MTH672

Course Title

Fluid Mechanics-II

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Determine relations between stress and rate of strain, coefficient of viscosity and laminar flow.

CO2: Apply the Navier-Stokes equations of motion of a viscous fluid, steady motion of viscous fluid between parallel planes and uniform circular cross-section and cross section in the form of circle, ellipse and equilateral triangle.

CO3:  Understand Energy dissipation due to viscosity, steady flow past a fixed sphere, dimensional analysis, Reynolds numbers, Prandtl’s boundary layer, Karman integral equation.

CO4: Understand elements of wave motion, waves in fluids, Surface gravity waves, standing waves, group velocity, energy of propagations, path of particles, waves at interface of two liquids.

Course Code

MTH673

Course Title

Algebraic Topology

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand the concepts of Homotopy classes and find the Fundamental Groups.

CO2: Learn the concepts of Deformation Retracts, Homotopy type and Homotopy invariance.

CO3: Find  the structure of the fundamental group of a topological space  in terms of the fundamental groups of open, path-connected subspaces and learn some  properties of groups.

CO4: Classify various covering spaces and check equivalence of covering spaces .

Course Code

MTH676

Course Title

Integral Equations-II

Course Outcomes

After successfully completing this course, the students will be able to

CO1: Understand Fredholm integro-differential equations, The Direct Computation Method, The Adomian Decomposition Method, The Modified Decomposition Method, The Noise Terms Phenomenon, The Variational Iteration Method, Converting to Fredholm Integral Equations.

CO2: Understand Volterra integro-differential equations, the Adomian Decomposition Method, The Variational Iteration Method, converting to Volterra Integral Equation, Converting to Initial Value Problems, Volterra in taro-Differential Equations of the First Kind.

CO3: Understand nonlinear Fredholm integral equations, The Direct Computation Method, The Adomian Decomposition Method, The Variational Iteration Method Nonlinear Fredholm Integral Equations of the First Kind, The Method of Regularization, Nonlinear Weakly-Singular Fredholm Integral Equations, The Modified ecomposition Method.

CO4: Understand nonlinear Volterra integral equations, and their solutions by the Series Solution Method, The Adomian Decomposition Method.  The Variational Iteration Method, Nonlinear Volterra Integral Equations of the First Kind, The Series Solution Method, Conversion to a Volterra Equation of the Second Kind, Nonlinear Weakly-Singular Volterra Integral Equations, The Modified Decomposition Method.