Program Educational Objectives (PEOs)
No. 
Attributes 
PLOs 
1 
Mathematics and Knowledge 
An ability to apply knowledge of Mathematics to address the industrial and everyday life problems. 
2 
Problem Analysis and Reasoning 
An ability to survey existing literature, identification of gaps, permissible solution of problems to substantiate conclusions. 
3 
Investigation Tools 
An ability to interact with methodological and computational advancements facilitating the permissible solutions. 
4 
Mathematics and Society 
An ability to demonstrate the applicability of mathematical rigors in modeling of complex social and health phenomena. 
5 
Dissemination 
An ability to communicate effectively the outcomes of Mathematical pathways. 
6 
Project Execution 
An ability to design and execute a research project as an independent researcher in a multidisciplinary environment. 
Program Structure and Course Contents
Code  Course Title  Credit Hours 

MA5001  Riemannian Geometry  3 
MA5002  Advanced Numerical Analysis  3 
MA5003  Advanced Partial Differential Equations  3 
MA5004  Fluid Mechanics  3 
Total  12 
Code  Course Title  Credit Hours 

MA50XX  Elective CourseI  3 
MA50XX  Elective CourseII  3 
MA50XX  Elective CourseIII  3 
MA50XX  Elective CourseIV  3 
TEX5078  Functional Textile  2 
Total  14 
Code  Course Title  Credit Hours 

MA5090  Research Thesis  6(3+3) 
Total Credit Hours of the Programme  32 
Sr. No. 
Code 
Course Title 
Credit Hours 
1 
MA5005 
Graph Theory 
3 (3, 0) 
2 
MA5006 
Integral Transform 
3 (3,0) 
3 
MA5007 
Numerical Solutions of Partial Differential Equations 
3 (3,0) 
4 
MA5008 
Compressible Fluid Flow 
3 (3, 0) 
5 
MA5009 
Viscous Fluid Flow 
3 (3, 0) 
6 
MA5010 
Cosmology 
3 (3, 0) 
7 
RM5011 
Research Methodology

3 (3, 0) 
Manifolds, Differential Maps, Submanifolds, Tangents, Coordinate Vector Fields, Tangent Spaces, Dual Spaces, Multilinear Functions, Algebra of Tensors, Vector Fields, Tensor Fields, Integral Curves, Flows, Lie Derivatives, Brackets, Differential Forms, Integration Theory on Manifolds, Riemannian and Semi Riemannian Metrics, Flat Spaces, Affine Connection, Parallel Translations, Covariant Differentiation of Tensor Fields, Curvature Tensor, Torsion Tensor, Connection of a SemiRiemannian Tensor, Killing Equation, Killing Vector Fields, Geodesics, Conformal Transformations, The Weyl Tensor.
Euler’s method, Improved and Modified Euler’s Method, RungeKutta Method, Milne’s Method, Hamming’s Methods, Initial Value Problem, Special Cases when First Derivative Missing, Boundary Value Problems, Simultaneous Algebraic Equations Method, Iterative Methods for Linear Equations, GaussSiedel Method, Relaxation Methods, Vector and Matrix Norms, Sequences and Series of Matrices, Graph Theory, Directed Graph of A Matrix, Strongly Connected and Irreducible Matrices, Grerschgoin Theorem, Symmetric and Positive Definite Matrices, CyclicConsistently Ordered Matrices, Choice of Optimum Value for Relaxation Parameter.
Cauchy’s Problems for Linear Second Order Equations in NIndependent Variables, Cauchy Kowalewski Theorem, Characteristics Surfaces, Adjoint Operations, Bicharacteristics Spherical, and Cylindrical Waves, Heat Equation, Wave Equation, Laplace Equation, Maximum Minimum Principle, Integral Transforms.
NavierStokes Equation and Exact Solutions, Dynamical Similarity and Reynold’s Number, Turbulent Flow, BoundaryLayer Concept and Governing Equations, Laminar Flat Plate, Boundary Layer, Exact Solution, Momentum, Integral Equation, Use of Momentum Integral Equation for Flow with Zero Pressure Gradient, Pressure Gradient in BoundaryLayer Flow, Reynold’s Equations of Turbulent Motion, Magnetohydrodynamics, MHD Equations, Fluid Drifts, Stability and Equilibrium Problems.
Fundamentals of Graph Theory, Paths, Cycles, Trees, Hamilton Cycles, Euler Circuits, Planer Graphs, Flows, Connectivity, Matching Network Flows, Connectivity and Menger’s theorem, External Problems, Paths, and Complete Subgraphs, Hamilton Path and Cycles, Coloring, Vertex Coloring, Edge Coloring, Graphs on Surfaces.
Laplace Transform, Applications to Integral Equations, Fourier Transforms, Fourier Sine and Cosine Transform, Inverse Transform, Applications to Differentiation, Convolutions Theorem, Applications to Partial Differential Equations, Hankel Transform and Its Applications, Applications to Integration, Mellin Transform and its Applications.
Recommended Books:
Boundary and Initial Conditions, Polynomial Approximations in Higher Dimensions, Finite Element Method, Galerkin Method in One and More Dimensions, Error Bound on Galerkin Method, The Method of Collocation, Error Bounds on The Collocation Method.
Recommended Books:
Introduction to inviscid compressible flow, Concepts of thermodynamics, Types of processes, Second law of thermodynamics, Energy equation, Stream function for steady compressible flow, Velocity of sound, Mach number, Types of compressible flows, Distinction between Subsonic and Supersonic flows, Isentropic and nonisentropic inviscid compressible flow, Flowthrough varyingarea ducts, Normal shock waves, Prandtl relation, Fanno flow, Rayleigh flow, the Hodograph method, Introduction to viscous compressible flow, NavierStokes equations for a viscous compressible flow, Energy equation for a viscous compressible flow, Basic equations for threedimensional viscous compressible flow, Exact solutions of NavierStokes equations for a viscous compressible flow, Boundary layer equation for twodimensional viscous compressible flow, Momental Integral equation.
Recommended Books:
Some examples of viscous flow phenomena, properties of fluids, boundary conditions, equation of continuity, the NavierStokes’ equations, the energy equation; boundary conditions, orthogonal coordinate system, dimensionless parameters, velocity considerations, twodimensional considerations, and the stream functions, Couette flows, Poissillee flow, unsteady duct flows, similarity solutions, some exact analytic solution from the paper, introduction to laminar boundary layers equations, similarity solutions, twodimensional solutions, thermal boundary layer, some exposure will also be given from the recent literature appearing in the journals.
Recommended Books:
Principles of Relativity: Overview of Special Relativity  spacetime interval and Lorentz metricfour vectors  Introduction to general relativity (GR)  equivalence principle  notions of curvature  gravitation as a manifestation of the curvature of spacetime  gravitational redshift and clock corrections  orbits in strong gravity, light bending and gravitational lensing  concept of horizon and ergosphere, hydrostatic equilibrium in GR  gravitational radiation. Cosmological Models: Universe at large scales – Homogeneity and isotropy – distance ladder – Newtonian cosmology  expansion and redshift  Cosmological Principle  Hubble’s law  RobertsonWalker metric  Observable quantities – luminosity and angular diameter distances  Horizon distance Dynamics of Friedman RobertsonWalker models: Friedmann equations for sources with p=wu and w =−1, 0, 1/3, discussion of closed, open and flat Universes.
Recommended Books:
Scientific Statements, Hypothesis, Model, Theory and Law, Types of Research, Problem Definition, Objectives of Research, Research Design, Data Collection, Data Analysis, Interpretation of Results, Validation of Results, Literature Search, Formal Research Proposal, Budgeting and Funding, Sampling, Systematic Sampling, Stratified Sampling, Cluster Sampling, Convenience Sampling, Judgment Sampling, Quota Sampling, Snow Ball Sampling, Identifying Variables of Interest and their Interactions, Operating Characteristic Curves, Power Curves, Surveys and Field Trials, Submission of a Paper, Role of Editor, PeerReview Process, Importance of Citations, Impact Factor, Plagiarism, Protection of Research Work from Misuse.
Recommended Books:
Basics of textiles and raw materials, Preparatory processes of Spinning, Types of yarns and spinning, Mathematical Modeling regarding fiber and yarn properties, Woven Fabric Production, Knitted Fabric Production, Mathematical Modeling regarding fiber, yarn, and woven fabric properties, Mathematical Modeling regarding fiber, yarn, and knitted fabric properties, Nonwoven fabric formation, and operations, Introduction to textile processing, Pretreatment and dyeing of textiles, Printing, and finishing of textiles, Application of mathematical modeling in textile processing, Clothing Product design, and development, Clothing preparatory processes, Clothing manufacturing processes, Applications of mathematical modeling in clothing.
Recommended Books:
The MS thesis will only be reviewed for evaluation when the research paper is “Under Review” or “Under Consideration” by a journal. The reviewer will be a PhD examiner of the relevant field from an external university/institute to evaluate the thesis in addition to the departmental evaluation committee. The Plagiarism test must be conducted on the dissertation before its submission to the external expert as per HEC criteria.
Mathematics enhances the analytical skills that help in almost all disciplines of life. In addition, it helps in problemsolving, logical thinking, and decisionmaking skills. Thus, a mathematician can avail several opportunities in data sciences, artificial intelligence, and areas related to research and development in engineering and science. Jobs directly related to your degree include:
Note: The student will submit his/her publication from his/her thesis research work and submit to his/her supervisor. Final defense will be held after the submitted publication of student will be notified as “Under Review” or “Under Consideration” by a journal. It will be compulsory for graduate student to include his/her Supervisor’s name in his/her publication.
Merit Criteria
Admission merit will be prepared according to the following criteria:
BS/MSc or Equivalent  60% weightage 
NTSGAT (General) Test  30% weightage 
Interview  10% weightage 
Fee Head  1st  2nd  3rd  4th 

Admission Fee (Once)  25000       
Certificate Verification Fee (Once)  2000       
University Security (Refundable)  5000       
Red Crescent Donation (Once)  100       
University Card Fee (Once)  300       
Degree Fee (Once)        5000 
Tuition Fee (Per Semester)  30,000  30,000  21,000  21,000 
Library Fee (Per Semester)  3000  3000  3000  3000 
Examination Fee (Per Semester)  3000  3000  3000  3000 
Medical Fee (Per Semester)  2000  2000  2000  2000 
Student Activity Fund (Per Semester)  2000  2000  2000  2000 
Endowment Fund (Per Semester)  1000  1000  1000  1000 
TOTAL  73,400  41,000  32,000  37,000 