M.Sc MatheMatics

Objectives This course will provide information about groups, sub groups, characteristics of a field, prime subfield and ideal theory in the polynomial ring. It also imparts knowledge about modules. Outcomes After completion of the course, the student will be able to: Explain the fundamental concepts of advanced algebra such as groups and rings and their role in modern mathematics and applied contexts. Demonstrate accurate and efficient use of advanced algebraic techniques.

Objectives This course will provide information about the properties of real numbers, series of real numbers. It also imparts knowledge about convergence and divergence of series, differentiability of real functions and related problems. Outcomes After completion of the course, the student will be able to: Understand the theoretical structures of basic concepts in analysis. Learn the foundational results in the fields of Real Analysis. Understand the theoretical foundation and properties of the Riemann Stieltjes integral, Pointwise convergence, Uniform convergence. Know the definition of Riemann Stieltjes integral, Pointwise convergence, Uniform convergence and how to determine the components of the convergence of a sequence as well as series. Apply the different type of tests to find the convergence. Understand Functions of several variables, Partial derivatives, directional derivatives, Jacobian and Lagrange's multiplier method. Students should know the importance of Real Analysis

Objectives This course will provide information about intense foundation in fundamental concepts of point-set topology Outcomes After completion of the course, the student will be able to: Work basic problems (proofs, construction of examples, counter-examples, or argue that a claim is false) in the Topology , Topology of Metric Spaces, Moore Spaces, Tychonoff spaces, and Hausdorff spaces. Familiar with separability, completeness, connectedness, compactness, densityand basis.

Objectives This course will provide information about the concepts of analyticity,Cauchy integral theorem in different domains. Students will be equippedwith the understanding of the fundamental concepts of complex variable theory. In particular,students will acquire the skill of contour integration to evaluate complicated real integrals viaresidue calculus. Outcomes After completion of the course, the student will be able to: Understand about the Cauchy-Riemann equations, analytic functions, entire functionsincluding the fundamental theorem of algebra Evaluate complex contour integrals and apply the Cauchy integral theorem in itsvarious versions, and the Cauchy integral formula. Analyze sequences and series of analytic functions and types of convergence Represent functions as Taylor and Laurent series, classify singularities and poles, find residues and evaluate complex integrals using the residue theorem.

Objectives This course will provide information about the excel software which help to manage the data and presenting the data in both mathematical and picture form. The representation of data in different forms of graphs and maintaining the data using advance option will be discussed. Outcomes After completion of the course, the student will be able to: Familiar with the software that helps to organize a vast amount of raw data into well organized meaningful information in minimal time frame.

Outcomes Seminar enhance the skills of students in presentation, discussion, listening, critical thinking, studying major work.

Objectives This course will provide information about the various results and methods for solving Ordinary Differential equation. It includes many theorems and significant results of first, second and higher order differential equations. Also, provide a brief introduction to Initial value and boundary value problems, Sturm-Liouville problems and autonomous system. Outcomes After completion of the course, the student will be able to: Familiar with various methods of solving Ordinary differential equations. Solve many Initial and Boundary value Problem exists in different fields of science. Study of autonomous system will helpful for qualitatively analysis of different types of Ordinary differential equations.

Objectives This course will provide information about Measurable sets, Measurable functions, Lebesgue Integral, Differentiation and Integration the Lebesgue Lp Spaces, their properties and also some of their fruitful applications. Outcomes After completion of the course, the student will be able to: understand how the Lebesgue measure on R is defined. understand basic properties are measurable functions. understand how the measures may be used to construct integrals. know the basic convergence theorems for the Lebesgue integral, understand the relation between differentiation and Lebesgue integration.

Seminar enhance the skills of presentation, discussion, listening, critical thinking etc.

Objectives This course will provide information about basic concepts of set theory, logic, proof techniques, binary relations, graph and trees. Outcomes After completion of the course, the student will be able to: Construct mathematical arguments using logical connectives and quantifiers. Validate the correctness of an argument using statement and predicate calculus. Understand how graphs and trees are used as tools and mathematical models in the study of networks. Learn how to work with some of the discrete structures which include sets, relations, functions, graphs and trees.

Objectives This course will provide information about the variation technique and mechanics that exists in different fields of science. Outcomes After completion of the course, the student will be able to: Solve the various Scientific problems based on the variations Familiarize with various theories of classical mechanics. Solve the various physics problems based on the classical mechanics.

This course will provide information about the latex software that helps to prepare the high quality document typesetting which is preferably used for mathematical and scientific papers for various journals. It Includes the basics of Latex software and various options used to prepare the manuscripts or chapters as the requirement of the journals and thesis formats. Outcomes: After completion of the course, the student will be able to: Familiar with the Latex software that helps to prepare their documents. Prepare the typesetting of journal article, technical report, thesis, books and slide presentation etc.

Seminars enhance the skills of students in resentation, discussion, listening, critical thinking etc.

Objectives This course will provide information about pure and applied Mathematics, with countless applications to the theory of differential equations, engineering, and physics. The students will be exposed to the theory of Banach spaces, the concept of dual spaces, the Hahn-Banach theorem, the axiom of choice and Zorn's lemma, Open mapping theorem, closed graph theorem. Inner product spaces, Hilbert spaces and their examples Outcomes After completion of the course, the student will be able to: Understand the fundamentals of functional analysis and the concepts associated with the dual of a linear space. Understand mathematical applications of Functional analysis in pure mathematics such as representation theory.

Objectives This course will provide information about various statistical tools for data analysis. Outcomes After completion of the course, the student will be able to use various statistical methods for data analysis

Objectives This course will provide information about solution of real life problems related to business using various optimization techniques. Outcomes After completion of the course, the student will be able to: Model engineering minima/ maxima problems as optimization problems. Use MATLAB to implement optimization algorithms.

Objectives This course will provide information about nature of a fluid, general analysis of fluid motion, the analysis of the behavior of fluids is based on the fundamental laws of mechanics which relate continuity of mass and energy with force and momentum together with the familiar solid mechanics properties. Outcomes After completion of the course, the student will be able to: Understand the basic principles of fluid mechanics, such as Lagrangian and Eulerian approach, conservation of mass etc. Use Euler and Bernoulli's equations and the conservation of mass to determine velocity and acceleration for incompressible and inviscid fluid. Understand the concept of rotational and irrotational flow, stream functions, velocity potential, sink, source, vortex etc. Analyse simple fluid flow problems( motion of Cylinders ) with Navier - Stoke's equation of motion.

Objectives This course will provide information about the Python software. It includes basics of python and formation of python program using python lists, python tuples and how to build the python files using special functions. Outcomes After completion of the course, the student will be able to: Familiar with the basics of python software. Prepare many programs with the use of python commands.

Objectives This course will provide information about the python environment. It includes the installation of python, basic and advanced programs based on mathematical form that helpful to understand the python formats. Outcomes After completion of the course, the student will be able to: Prepare many mathematical programs with the use of python software. learn plotting of many types of graphs in python environment.

Seminars enhance the skills of students in resentation, discussion, listening, critical thinking etc.

Objectives This course will provide information about stress and strain of materials, properties of area, principal axes and moments of inertia, tension and compression, strain energy, torsion. Outcomes After completion of the course, the student will be able to: Understand the concepts of stress at a point, strain at a point, and the stress-strain relationships for linear elastic, homogeneous, isotropic materials. To determine principal stresses and angles, maximum shearing stresses and angles, and the stresses acting on any arbitrary plane within a structural element. To utilize basic properties of materials such as elastic moduli and Poisson's ratio to appropriately to solve problems related to isotropic elasticity. Understand affine transformations and geometrical interpretation of the components of strain and terms related to strain tensor. Understand the generalized Hooke’s law, reduction of elastic constants to different elastic models from the most general case. Develop equili

This course will provide information about the integral equation that exists in different fields of science

This course will provide information how to solve real life problems related to business using various optimization techniques. Outcomes: After completion of the course, the student will be able to: Identify and develop operational research models from the verbal description of the real system, Understand the mathematical tools that are needed to solve optimization problems, Use mathematical software to solve the proposed models. Develop a report that describes the model and the solving technique, analyze the results and purpose recommendations in language understandable to the decision-making processes in Management Engineering

Objectives This course will provide information about Integral transforms so that the knowledge can be used in different fields of Science and Engineering. Outcomes After completion of the course, the student will be able to: Apply Laplace Transformation to solve initial and boundary value problems. Learn Fourier transformation and their applications to relevant problems. Understand Hankel's Transformation to solve boundary value problem.

Objectives This course will provide information about MATLAB software, to enable the student to carry out simple numerical computations and analysis using MATLAB Outcomes After completion of the course, the student will be able to: Understand the syntax, semantics, data-types and library functions. Solve the mathematical equations using different commands and functions. Interpret and visualize simple mathematical functions and operations thereon using plots/display.

Outcomes Seminar enhance the skills of students in presentation, discussion, listening, critical thinking, studying major work.