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 |
|---|---|---|
| MA-5001 | Riemannian Geometry | 3 |
| MA-5002 | Advanced Numerical Analysis | 3 |
| MA-5003 | Advanced Partial Differential Equations | 3 |
| MA-5004 | Fluid Mechanics | 3 |
| Total | 12 | |
| Code | Course Title | Credit Hours |
|---|---|---|
| MA-50XX | Elective Course-I | 3 |
| MA-50XX | Elective Course-II | 3 |
| MA-50XX | Elective Course-III | 3 |
| MA-50XX | Elective Course-IV | 3 |
| TEX-5078 | Functional Textile | 2 |
| Total | 14 | |
| Code | Course Title | Credit Hours |
|---|---|---|
| MA-5090 | Research Thesis | 6(3+3) |
| Total Credit Hours of the Programme | 32 | |
|
Sr. No. |
Code |
Course Title |
Credit Hours |
|
1 |
MA-5005 |
Graph Theory |
3 (3, 0) |
|
2 |
MA-5006 |
Integral Transform |
3 (3,0) |
|
3 |
MA-5007 |
Numerical Solutions of Partial Differential Equations |
3 (3,0) |
|
4 |
MA-5008 |
Compressible Fluid Flow |
3 (3, 0) |
|
5 |
MA-5009 |
Viscous Fluid Flow |
3 (3, 0) |
|
6 |
MA-5010 |
Cosmology |
3 (3, 0) |
|
7 |
RM-5011 |
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 Semi-Riemannian Tensor, Killing Equation, Killing Vector Fields, Geodesics, Conformal Transformations, The Weyl Tensor.
Euler’s method, Improved and Modified Euler’s Method, Runge-Kutta 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, Gauss-Siedel 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, Cyclic-Consistently Ordered Matrices, Choice of Optimum Value for Relaxation Parameter.
Cauchy’s Problems for Linear Second Order Equations in N-Independent Variables, Cauchy Kowalewski Theorem, Characteristics Surfaces, Adjoint Operations, Bicharacteristics Spherical, and Cylindrical Waves, Heat Equation, Wave Equation, Laplace Equation, Maximum- Minimum Principle, Integral Transforms.
Navier-Stokes Equation and Exact Solutions, Dynamical Similarity and Reynold’s Number, Turbulent Flow, Boundary-Layer 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 Boundary-Layer 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 non-isentropic inviscid compressible flow, Flow-through varying-area ducts, Normal shock waves, Prandtl relation, Fanno flow, Rayleigh flow, the Hodograph method, Introduction to viscous compressible flow, Navier-Stokes equations for a viscous compressible flow, Energy equation for a viscous compressible flow, Basic equations for three-dimensional viscous compressible flow, Exact solutions of Navier-Stokes equations for a viscous compressible flow, Boundary layer equation for two-dimensional viscous compressible flow, Momental Integral equation.
Recommended Books:
Some examples of viscous flow phenomena, properties of fluids, boundary conditions, equation of continuity, the Navier-Stokes’ equations, the energy equation; boundary conditions, orthogonal coordinate system, dimensionless parameters, velocity considerations, two-dimensional 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, two-dimensional 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 - Robertson-Walker metric - Observable quantities – luminosity and angular diameter distances - Horizon distance- Dynamics of Friedman- Robertson-Walker 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, Peer-Review 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 problem-solving, logical thinking, and decision-making 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 to his/her supervisor. Final thesis defense of student will be held after the submission of publication to a relevant HEC recognized 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 |
| NTU-GAT (General) Test | 30% weightage |
| Interview | 10% weightage |
| Programs | Total One Time Dues at Admission (Rupees) | Tuition Fee (1st Semester) (Rupees) | Total Other Charges (Per Semester) (Rupees) | Total 1st Semester Dues (Rupees) |
| M.S. Mathematics | 32,400 | 37,630 | 11,000 | 81,030 |
| Particulars | Rupees |
| Admission Fee (Once at admission) | 25,000 |
| Certificate Verification Fee (Once at admision) | 2,000 |
| University Security (Refundable) | 5,000 |
| Red Crescent Donation (Once at admision) | 100 |
| University Card Fee (Once at admision) | 300 |
| Library Fee (Per Semester) | 3,000 |
| Examination Fee (Per Semester) | 3,000 |
| Medical Fee (Per Semester) | 2,000 |
| Student Activity Fund (Per Semester) | 2,000 |
| Endowment Fund (Per Semester) | 1,000 |
| Degree Fee (Once in the Last Semester) | 5,000 |
| Total | 32,400 |
| Particulars | Rupees |
|---|---|
| Hostel Charges (Per Semester) | 25,000 |
| Hostel Security (Refundable) | 5,000 |
| TOTAL | 30,000 |