M.Sc. Mathematics
The MSc Mathematics course is designed in such a way that permits the students to enhance their skills and knowledge on fundamental as well as advanced levels of mathematics. The gained knowledge is further nourished with various industry oriented courses taught in mode of value added courses.
| Duration | 2 Years |
| Fees PA | 99000/- |
| Eligibility Criteria | Pass in B.Sc. or B.Sc. (Hons.) with 50% or more marks in relevant subjects. |
| Merit Preparation for Admission | Merit preparation/ short listing of candidates shall be on the basis of score in MRNAT 2024/ Graduation Qualifying Examination. |
CO-PO Mapping Click Here
To elaborate their research skills and to evolve their potential in writing research papers Scientific research is introduced in second and third semester, which involves identifying the problem, survey of literature, critical thinking, planning of experiment and execution followed by presentation of their work via seminars, poster/oral presentation in conferences and finally reporting and defending their master’s dissertation.
Program Educational Objectives
Preparation: A broad general education ensuring an adequate foundation in Basic Sciences, and the English language
Core Competence: A solid understanding of concepts fundamental to the discipline of Sciences.
Breadth: Good analytical skills, design, and implementation of science experiments required to solve current scientific and societal problems.
Professionalism: The ability to function and communicate effectively the key knowledge base and laboratory resources careers as professionals.
Learning Environment: To provide student awareness of the Sciences as an integral activity for addressing social, economic, and environmental problems, and fostering important skills for jobs as well as for higher studies.
Programme Outcomes
After the completion of the program, the students will:
PO1 Knowledge & Abstract thinking: Ability to absorb and understand the abstract concepts that lead to various advanced theories in mathematical sciences and their applications in real life problems.
PO2 Modelling and solving: Ability in modelling and solving problems by identifying and employing the appropriate existing theories and methods.
PO3 Advanced theories and methods: Understand advanced theories and methods to design solutions for complex mathematical problems and results.
PO4 Applications in Engineering and Sciences: Understand the role of mathematical sciences and apply the same to solve real-life problems in various fields of study.
PO5 Modern software tool usage: Acquire the skills in handling scientific tools towards problem solving and solution analysis.
PO6 Ethics: Imbibe ethical, moral and social values in personal and social life. Continue to enhance the knowledge and skills in mathematical sciences for constructive activities and demonstrate the highest standards of professional ethics.
PO7 Individual and team work: Function effectively as an individual, and as a member or leader in diverse teams, and in multidisciplinary settings.
PO8 Communication: Develop various communication skills such as reading, listening, and speaking which will help in expressing ideas and views clearly and effectively.
PO9 Research: Demonstrate knowledge, understand mathematical & scientific theories and apply these to one’s own work, as a member/ leader in a team to manage projects and multidisciplinary research environments. Also use the research-based knowledge to analyse and solve advanced problems in mathematical sciences.
PO10 Life-long learning: Recognize the need for, and have the preparation and ability to engage in independent and life-long learning .
PO11 Professional Growth: Keep on discovering new avenues in the chosen field and exploring areas that remain conducive for research and development
Key Features:
- Extensive & latest academic curriculum
- CBCS (Choice Based Credit System)
- A wide range of core and open elective courses as per Industry requirements
- Problem-based learning through dissertation.
- Mandatory Internships for students.
- Outcome based teaching with hands on Lab sessions
- Exposure of students to present their research work in various National/International Conferences / Workshops / Seminars.
- Placement oriented technical and soft skill training sessions.
- Regular International & National invited Lectures/ workshops etc. from Academia & Industry
- Quantitative aptitude sessions for competitive exams.
- Imbibing new ideas through educational visits.
CO-PO Mapping
| DEPARTMENT OF SCIENCES-MATHEMATICS | ||||||||||||||
| M.Sc Mapping of COs with POs | ||||||||||||||
| Instructions to fill the mapping matrix: 1. Fill grade 1,2,3 for Low, Medium, High respectively, as per the level of mapping between course and relevant POs or PSOs. In case if CO does not map with any of the PO or PSO, you are requested to put “”. 2. Add or delete rows as per the number of COs in your respective course, wherever required. As of now, there are four rows allocated to each course. |
||||||||||||||
| SEMESTER-I | ||||||||||||||
| Courses Code | Courses | Course Outcomes | CO Statement | PO1 | PO2 | PO3 | PO4 | PO5 | PO6 | PO7 | PO8 | PO9 | PO10 | PO11 |
| MAH514B | ABSTRACT ALGEBRA | CO1 | To elaborate the algebraic structure with two binary operations such as Ring and Fields. | 3 | 3 | 1 | 2 | 1 | 3 | 3 | 1 | |||
| CO2 | To characterize the polynomials over ring and fields. | 3 | 3 | 1 | 2 | 1 | 3 | 3 | 1 | |||||
| CO3 | To identify and construct example of modules and their application to finitely generated abelian groups. | 3 | 3 | 1 | 2 | 1 | 3 | 3 | 1 | |||||
| CO4 | To define and characterize Notherian, Artinian module, and their applications in structure theorem. | 3 | 3 | 1 | 2 | 1 | 3 | 3 | 1 | |||||
| MAH502B | TOPOLOGY-I | CO1 | Understand terms, definitions and theorems related to topology. | 3 | 2 | 1 | 2 | 1 | 3 | 3 | 2 | |||
| CO2 | Demonstrate concepts of topological space such as open and closed sets, interior, closure and boundary. | 3 | 2 | 1 | 2 | 1 | 3 | 3 | 2 | |||||
| CO3 | Create new topological spaces by using subspace, product and quotient topologies. | 3 | 2 | 3 | 1 | 2 | 1 | 3 | 3 | 2 | ||||
| CO4 | Use continuous functions and homeomorphisms to understand structure of topological spaces. | 3 | 2 | 3 | 1 | 2 | 1 | 3 | 3 | 2 | ||||
| CO5 | Apply theoretical concepts of topology to real world applications. | 3 | 2 | 3 | 1 | 2 | 3 | 2 | ||||||
| MAH503B | DIFFERENTIAL EQUATIONS | CO1 | Illustrate the basic concept of differential equations | 3 | 2 | 3 | 1 | 2 | 3 | 2 | ||||
| CO2 | Explain the various techniques to solve the different types of differential equations | 3 | 2 | 3 | 1 | 2 | 3 | 2 | ||||||
| CO3 | To Understand and apply concept of power series technique to solve the differential equations | 3 | 2 | 3 | 1 | 2 | 3 | 2 | ||||||
| CO4 | Apply the concepts of differential equations in various physical problems (heat equations, wave equations | 3 | 2 | 2 | 1 | 2 | 3 | 2 | ||||||
| MAH504B | MEASURE THEORY | CO1 | demonstrate the underlying concepts of algebra’s of sets, Measure Space, Lebesgue measure space, measurable and nonmeasurable functions. | 3 | 3 | 2 | 3 | 3 | ||||||
| CO2 | appply the basic concepts Lebesgue integral to solve related mathematical Problems . | 3 | 3 | 2 | 3 | 3 | ||||||||
| CO3 | describe and apply the notion of measurable functions and sets and use Lebesgue monotone and dominated convergence theorems and Fatous Lemma. | 3 | 3 | 2 | 3 | 3 | ||||||||
| CO4 | describe the construction of product measures and use of Fubini’s theorem | 3 | 3 | 2 | 3 | 3 | ||||||||
| MAH512B | MATHEMATICAL STAITISTICS | CO1 | Use and apply the concepts of probability mass/density functions for the problems involving single/bivariate random variable |
1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 |
| CO2 | Explain concept of Estimation and their properties | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| CO3 | Apply testing of hypothesis, types of error and test of significance for different sample sizes. | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| CO4 | Demonstrate an ability to apply statistical tools to solve problems. | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| MAW515B | EXCEL WORKSHOP | CO1 | Comprehend effective use of appropriate spreadsheet vocabulary. | 2 | 3 | 1 | 3 | |||||||
| CO2 | Use critical thinking and problem solving skills in designing the spreadsheets for various business problems. | 2 | 3 | 1 | 3 | |||||||||
| CO3 | Assess the document for accuracy in the entry of data and creation of formulas, readability and appearance. | 2 | 3 | 1 | 3 | |||||||||
| CO4 | Develop efficiency with specific sets of skills through repetitive reinforcement to evaluate business problems | 2 | 3 | 1 | 3 | |||||||||
| MAH506B | MATHEMATICS LAB-I | CO1 | To perform basic mathematical calculations, plotting the graphs and matrix operation using Mathematical software. | 1 | 3 | 3 | 2 | |||||||
| CO2 | To evaluate derivative and its application using mathematical software. | 1 | 3 | 3 | 2 | |||||||||
| CO3 | To understand and apply concept of integration to evaluate area and volume using Mathematicalsoftware | 1 | 3 | 3 | 2 | |||||||||
| CO4 | To visualize and find the roots of quadratic, cubic & biquadratics equations and transformation of equations using mathematical software. |
1 | 3 | 3 | 2 | |||||||||
| CSH511B | PYTHON PROGRAMMING |
CO1 | Install and run the Python interpreter | 1 | 3 | |||||||||
| CO2 | Create and execute Python programs | 1 | 3 | 3 | ||||||||||
| CO3 | Describe how to program using Python, by learning concepts like variables, flow controls, data types, type conversion | 1 | 3 | 2 | 1 | |||||||||
| CO4 | Implement python data structures | 1 | 2 | 2 | 3 | 1 | ||||||||
| CO5 | Understand the concepts of file I/O | 1 | 2 | 3 | 2 | |||||||||
| CO6 | Solve problems using functions, objects and classes | — | 2 | 1 | 1 | 2 | 1 | 2 | 2 | 2 | ||||
| CDO511 | PROFESSIONAL COMPETENCE PG | CO1 | Students will be able to recognize problems based on arithmetic & number systems. | 3 | 2 | 2 | 2 | 1 | 1 | — | — | 1 | — | — |
| CO2 | Students will be able to solve problems based on verbal reasoning & simplification. | — | — | — | 2 | 1 | — | — | — | — | 1 | — | ||
| CO3 | Students will be able to solve complex problems based on arithmetic reasoning. | 2 | 3 | 1 | 1 | 2 | 1 | — | — | 1 | — | — | ||
| CO4 | Students will be able to plan their career meticulously by setting their time oriented goals. | — | – | — | – | 1 | 1 | — | 1 | — | 1 | 1 | ||
| Total | 55 | 26 | 42 | 38 | 12 | 12 | 33 | 26 | 63 | 58 | 28 | |||
| SEMESTERII | ||||||||||||||
| Courses Code | Courses | Course Outcomes | CO Statement | PO1 | PO2 | PO3 | PO4 | PO5 | PO6 | PO7 | PO8 | PO9 | PO10 | PO11 |
| MAH517B | MATHEMATICAL MODELLING | CO1 | Understand various techniques of mathematical modeling | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 |
| CO2 | Apply mathematical models in different fields and situations | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| CO3 | Understand and apply mathematical modeling through differential equations. | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| CO4 | Analyze Stochastic models and their needs. | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| MAH508B | COMPLEX ANALYSIS | CO1 | Understand the significance of continuity, differentiability and analyticity of complex functions | 1 | 2 | 3 | 2 | 2 | 2 | 2 | 2 | 2 | ||
| CO2 | Demonstrate the use of Cauchy integral formula ,Taylor and Laurent series expansions. | 3 | 2 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | ||||
| CO3 | Classify the nature of singularities, poles and residues and explain the application of Cauchy Residue theorem | 3 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 2 | ||||
| CO4 | Apply the consequences of analytic continuation, Schwarz reflection principle, Monodromy theorem and conformal mapping | 3 | 3 | 2 | 1 | 2 | 1 | 2 | 2 | 1 | ||||
| MAH509B | FUNCTIONAL ANALYSIS | CO1 | demonstrate the basic concepts, underlying the definition of the general Functional spaces like Norm Linear space, Quotient space, Banach space, Inner product spaces, Hilbert spaces. | 3 | 1 | 2 | – | – | – | 2 | 1 | 2 | 2 | – |
| CO2 | understand the concept associated with the dual of a linear space, point set topology, linear functional, linear operator, approximation theory. | 3 | 2 | 2 | – | – | – | 2 | 2 | 3 | 3 | – | ||
| CO3 | apply and understand the concept of HahnBanach Theorem and their applications, open mapping, closed graph theorems and weak topology. | 2 | 2 | 2 | – | – | – | 2 | 2 | 3 | 3 | – | ||
| CO4 | analysis the concept of orthonormal bases, complete orthonormal sets, Projection theorem, Riesz representation theorem, RieszFischer theorem. | 3 | 2 | 3 | – | – | – | 2 | 2 | 3 | 3 | – | ||
| MAH510B | DIFFERENTIAL GEOMETRY | CO1 | understand and evaluate mathematical problems based on the transformation of coordinate system, tensor Calculus | 1 | – | 3 | 2 | – | – | – | – | 2 | 2 | – |
| CO2 | understand, visualize and solve the problem related to Differentiable curves in R3 and their parametric representations |
1 | – | 3 | 2 | – | – | – | – | 2 | 2 | – | ||
| CO3 | visualize and apply the concepts to solve the problem related to Curvatures(Normal, Principal,Gaussian,Mean) and differential forms |
1 | – | 3 | 2 | – | – | – | – | 2 | 2 | – | ||
| CO4 | Understand and apply the concept of different operators on surface to solve the problem related to Minimal & totally umbilical surface, Geodesics. | 1 | – | 3 | 2 | – | – | – | – | 2 | 2 | – | ||
| MAH604B | OPERATIONS RESEARCH | CO1 | Understand any real life system with limited constraints and depict it in a model form. | 3 | 1 | 2 | 2 | 1 | 2 | 2 | 2 | |||
| CO2 | demonstrate the problem on the basis of obtained solution of different problems of OR with real world limitations/applications. | 3 | 2 | 2 | 2 | 2 | 3 | 3 | 2 | |||||
| CO3 | apply the different methods to solve OR problems & find the optimal solution. | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 2 | |||||
| CO4 | analyse and construct the mathematical models and learn to apply the restrictions on problems. | 3 | 2 | 3 | 2 | 2 | 3 | 3 | 2 | |||||
| MAH516B | MATHEMATICS LAB-II | CO1 | Write programming codes using conditional statements for related mathematical problems. | 3 | 2 | |||||||||
| CO2 | Write programming codes using iterative statements (for loop, while loop) for related mathematical problems. | 3 | 2 | |||||||||||
| CO3 | Successfully install LaTeX and its related components on a home/personal computer. | 2 | ||||||||||||
| CO4 | Use LaTeX and various templates acquired from the course to compose Mathematical documents, presentations, and reports | 3 | 2 | 2 | ||||||||||
| CO5 | Write mathematical documents containing mathematical expressions & formulas via LaTeX. | 3 | 2 | |||||||||||
| CO6 | Write articles in different journal styles. | 3 | 2 | 2 | ||||||||||
| CO7 | Draws graphs and figures in LaTeX. Customize LaTeX documents. | 3 | 2 | |||||||||||
| CO8 | Prepare presentations using LaTeX | 3 | 2 | 2 | ||||||||||
| CSH519B | PYTHON FOR DATA ANALYSIS | CO1 | Understanding of advance features of python programming . | 1 | 3 | 3 | ||||||||
| CO2 | Apply advance features of python programming for explorateory Analysis. | 1 | 3 | 2 | 1 | |||||||||
| CO3 | Implemant the concepts in various real world proplems | 1 | 2 | 2 | 3 | 1 | ||||||||
| CO4 | Perform Analysis through visualization | 1 | 2 | 3 | 2 | |||||||||
| RDO504 | SCIENTIFIC RESEARCH-I | CO1 | describe research and its impact. | 3 | 3 | 3 | 3 | |||||||
| CO2 | identify broad area of research, analyze, the processes and procedures to carryout research. | 3 | 2 | 3 | 3 | 2 | 3 | 3 | 3 | |||||
| CO3 | use different tools for literature survey | 3 | 3 | 2 | 2 | |||||||||
| CO4 | understand and adopt the ethical practice that are to be followed in the research activities. | 3 | 3 | 2 | 1 | |||||||||
| CO5 | work in groups with guidance. | 3 | 3 | 2 | ||||||||||
| CDO503 | PROFESSIONAL COMPETANCE PG-I | CO1 | Students will be able to recognize problems based on arithmetic & number systems. | 3 | 2 | 2 | 2 | 1 | 1 | — | — | 1 | — | — |
| CO2 | Students will be able to solve problems based on verbal reasoning & simplification. | — | — | — | 2 | 1 | — | — | — | — | 1 | — | ||
| CO3 | Students will be able to solve complex problems based on arithmetic reasoning. | 2 | 3 | 1 | 1 | 2 | 1 | — | — | 1 | — | — | ||
| CO4 | Students will be able to plan their career meticulously by setting their time oriented goals. | — | – | — | – | 1 | 1 | — | 1 | — | 1 | 1 | ||
| Total | 53 | 43 | 60 | 25 | 31 | 12 | 25 | 43 | 59 | 66 | 27 | |||
| SEMESTER-III | ||||||||||||||
| Courses Code | Courses | Course Outcomes | CO Statement | PO1 | PO2 | PO3 | PO4 | PO5 | PO6 | PO7 | PO8 | PO9 | PO10 | PO11 |
| MAH601B | INTEGRAL EQUATIONS & CALCULUS OF VARIATION | CO1 | Acquire sound knowledge of different types of Integral equations: Fredholm and Volterra integral equations. | 3 | 1 | 1 | 3 | – | – | – | – | 2 | 2 | 2 |
| CO2 | Deduce & solve integral equation from differential equation arising in different engineering branches | 2 | 2 | 3 | 2 | – | – | – | – | 2 | 1 | 1 | ||
| CO3 | Construct Green function in solving boundary value problem by converting it to an integral equation | 3 | 3 | 2 | 3 | – | – | – | – | 1 | – | 2 | ||
| CO4 | Identify functional and its applications in engineering problem. | 2 | 3 | 2 | 3 | – | – | – | – | 2 | 1 | 2 | ||
| CO5 | Use Euler-Lagrange equation or its first integral to find & solve differential equations for stationary paths subject to boundary conditions. | 3 | 2 | 2 | 3 | – | – | – | – | 2 | 1 | 2 | ||
| MAH602B | FLUID DYNAMICS | CO1 | Describe a continuum model of fluid flow and classify fluid/flows based on physical properties of a fluid/flow along with Eulerian and Lagrangian descriptions of fluid motion. | 3 | – | 3 | 3 | – | – | 2 | 2 | 1 | 1 | 1 |
| CO2 | Demonstrate an ability to apply the concepts of Steady viscous flow and Conservation of Momentum for solving real world problems | 3 | 3 | 3 | 3 | – | – | 2 | 2 | 1 | 1 | 1 | ||
| CO3 | Apply the concepts of rotational/rotational Motion for solving real world problems. | 3 | 3 | 3 | 3 | – | – | 2 | 2 | 1 | 1 | 1 | ||
| CO4 | Construct and Analyse mathematically the nature of Laminar/Non Laminar flow. | 3 | 3 | 3 | 3 | – | – | 2 | 2 | 1 | 1 | 1 | ||
| MAH607B | FOURIER ANALYSIS | CO1 | Understand the basic properties of Fourier series | 3 | – | 1 | 2 | – | – | – | – | – | 1 | – |
| CO2 | Use concept of separation of variables Sturm-Liouville Theorem to solve related problem | 3 | – | 2 | 2 | – | – | – | – | – | 1 | – | ||
| CO3 | Apply the concepts of distributions and Fourier transform to solve related problem | 3 | 3 | 2 | 2 | – | – | 2 | – | 1 | 2 | – | ||
| CO4 | Understand the application of Fourier transform | 3 | 3 | 3 | 3 | 1 | – | 2 | – | 2 | 2 | – | ||
| MAH507B | FIELD THEORY | CO1 | Explain the fundamental concepts of field extensions and its role in modern mathematics and applied contexts | 3 | 2 | – | – | – | 2 | – | 2 | 3 | 2 | – |
| CO2 | Demonstrate the application of Galois theory. | 3 | 2 | – | – | – | 2 | – | 2 | 2 | 2 | – | ||
| CO3 | Illustrate about Galois fields, Cyclotomic extension and polynomials | 3 | 2 | – | – | – | 2 | – | 2 | 2 | 2 | – | ||
| CO4 | Solve polynomial equations by radicals along with the understanding of ruler and compass | 3 | 2 | 1 | 1 | 2 | – | 2 | 2 | 2 | 2 | |||
| MAH608B | DIFFERENTIABLE MANIFOLDS | CO1 | Able to use concepts of tangent vectors and normal vectors to investigate intrinsic and extrinsic properties of differential manifolds | 1 | – | 2 | – | – | – | – | – | 2 | 2 | – |
| CO2 | Able to apply properties Lie bracket , Jacobian , transformation to establish results on differentiable manifolds. | 1 | – | 2 | – | – | – | – | – | 1 | 1 | – | ||
| CO3 | able to apply the concepts of immersion and submersion to study geometry of differential manifolds | 1 | – | 2 | – | – | – | – | – | 2 | 2 | – | ||
| CO4 | apply the concepts covariant derivative , curvature, connectedness to geometry of differential manifolds | 1 | – | 2 | – | – | – | – | – | 2 | 2 | – | ||
| MAH606B | DESIGN OF EXPERIMENTS | CO1 | understand the issues and principles of Design of Experiments (DOE) | 1 | 2 | – | – | – | – | 3 | 2 | – | – | – |
| CO2 | understand experimentation is a process | 1 | 2 | – | – | – | – | 3 | 2 | – | – | – | ||
| CO3 | list the guidelines for designing experiments | 1 | 2 | – | – | – | – | 3 | 2 | – | – | – | ||
| CO4 | construct BIBD | 1 | 2 | – | – | – | – | 3 | 2 | – | – | – | ||
| MAH623B | ADVANCED NUMERICAL ANALYSIS | CO1 | To Learn about errors which arise during computation due to roundoff or truncation or number representation and the high-end numerical methods for solving transcendental and polynomial equations. |
3 | 3 | 2 | 1 | 1 | 3 | 3 | 1 | |||
| CO2 | Attain the skills of solving system of linear equations using direct and iterative schemes and analysis of such schemes. Know to apply finite difference schemes/operators for numerical differentiation. |
3 | 3 | 2 | 1 | 1 | 3 | 3 | 1 | |||||
| CO3 | Learn advanced numerical methods to evaluate integrals for solving linear/non-linear first/second order IVP/BVP involving ODEs. |
3 | 3 | 2 | 1 | 1 | 3 | 3 | 1 | |||||
| CO4 | Understand the finite difference methods for solving parabolic, elliptic and hyperbolic PDEs and attain capability to use such methods in scientific problem solving. |
3 | 3 | 2 | 1 | 1 | 3 | 3 | 1 | |||||
| MAH614B | ADVANCED OPERATIONS RESEARCH | CO1 | Understanding of advance operations research techniques , methodologies and tools. | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| CO2 | Analyze and solve of the fundamental concepts and techniques used in Network Analysis. | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ||
| CO3 | Develop mathematical skills to analyze and solve OR models like Queueing, Replacement, etc and apply them for optimization. |
3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ||
| CO4 | Conduct and interpret post-optimal and sensitivity analysis and explain the primal -dual relationship. | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ||
| MAH625B | FUZZY SETS AND APPLICATIONS | CO1 | Understand the concept of fuzziness involved in various systems and fuzzy set theory | 3 | – | 1 | 2 | – | – | – | – | – | 1 | – |
| CO2 | Apply the concepts of fuzzy relation to solve related problem | 3 | – | 2 | 2 | – | – | – | – | – | 1 | – | ||
| CO3 | Use the concepts of fuzzy measure to understand physical problem related to different classes of fuzzy measures | 3 | 3 | 3 | 2 | – | – | 2 | – | 1 | 2 | – | ||
| CO4 | Analyze the application of fuzzy logic control to real time systems. | 3 | 3 | 3 | 3 | 1 | – | 2 | – | 2 | 2 | – | ||
| MAH605B | GRAPH THEORY | CO1 | Apply the concepts of path, walk , circuit to study different types of graph | 2 | 1 | – | – | – | – | 1 | – | 2 | – | – |
| CO2 | Apply concepts of tree to find the problem related to distance, spanning tree or minimal spanning tree | 2 | 1 | – | – | – | – | 2 | – | 2 | – | – | ||
| CO3 | Apply the concepts of shortest distance in graph to find the solution of problem of travelling saleman | 2 | 1 | – | – | – | – | 2 | – | 2 | – | – | ||
| CO4 | Understand the concept of coloring and planar graph | 2 | 1 | – | – | – | – | 2 | – | 2 | – | – | ||
| MAH609B | WAVELETS | CO1 | understand STFT, windowed Fourier transform, FT, IFT and difference between windowed Fourier transform and wavelet transforms. | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| CO2 | analyse and apply wavelet basis and characterize continuous and discrete wavelet transforms. | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | |||
| CO3 | construct wavelets by multiresolution analysis and identify various wavelets and evaluate their time frequency resolution properties. | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 3 | 3 | 3 | |||
| CO4 | Characterize Wavelets, MRA wavelets, Scaling function Lowpass filter & High Pass filter, MSF wavelets. | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 3 | 3 | 3 | |||
| MAH610B | TOPOLOGY-II | CO1 | Understand the product of two topological spaces and their properties | 3 | 3 | 2 | – | – | – | 1 | 2 | 1 | 3 | 3 |
| CO2 | Apply the concepts nets and filter to solve related problems | 3 | 3 | 2 | – | – | – | 1 | 2 | 1 | 3 | 3 | ||
| CO3 | Uses the notion of compactness to solve related problem | 3 | 3 | 2 | 3 | – | – | 1 | 2 | 1 | 3 | 3 | ||
| CO4 | Apply the concept of paracompactness to study study properties of product manifolds | 3 | 3 | 2 | 3 | – | – | 1 | 2 | 1 | 3 | 3 | ||
| RDO604 | SCIENTIFIC RESEARCH II | CO1 | able to critically evaluate the work done by various researchers relevant to the research topic. | 3 | 1 | 2 | 3 | 3 | ||||||
| CO2 | integrate the relevant theory and practices followed in a logical way and draw appropriate conclusions. |
3 | 2 | 2 | 3 | 3 | ||||||||
| CO3 | understand the research methodologies/approaches/techniques used in the literature. | 3 | 3 | 2 | 3 | 3 | ||||||||
| CO4 | structure and organize the collected information or findings through an appropriate abstract, headings, reference citations and smooth transitions between sections. | 3 | 2 | 3 | 3 | |||||||||
| RDO604 | SCIENTIFIC RESEARCH – II | CO1 | able to critically evaluate the work done by various researchers relevant to the research topic. | 3 | 1 | 2 | – | – | – | – | – | 3 | 3 | – |
| CO2 | integrate the relevant theory and practices followed in a logical way and draw appropriate conclusions. | 3 | 2 | 2 | – | – | – | – | – | 3 | 3 | – | ||
| CO3 | understand the research methodologies/approaches/ techniques used in the literature. | 3 | 3 | 2 | – | – | – | – | – | 3 | 3 | – | ||
| CO4 | structure and organize the collected information or findings through an appropriate abstract, headings, reference citations and smooth transitions between sections. | 3 | – | 2 | – | – | – | – | – | 3 | 3 | – | ||
| CDO603 | PROFESSIONAL COMPETANCE PG-II | CO1 | Students will be able to demonstrate problem solving and leadership skills required to participate in a stimulated environment. | 2 | — | 1 | 1 | 2 | 3 | — | 1 | 1 | 1 | |
| CO2 | Students will be able to face real life challenges using critical reasoning skills. | — | 2 | — | 2 | 1 | 1 | — | — | — | 1 | 1 | ||
| CO3 | Prepare for placements and manage interviews effectively. | — | — | — | — | — | — | — | 3 | — | 1 | 1 | ||
| CO4 | Enhance their ability to write, read, comprehend and communicate effectively to increase the productivity of business. | — | – | — | – | — | — | 1 | 3 | 1 | 2 | 1 | ||
| Total | 149 | 104 | 105 | 78 | 16 | 35 | 63 | 58 | 104 | 108 | 54 | |||
| SEMESTER-IV | ||||||||||||||
| Courses Code | Courses | CO Statement | CO Statement | PO1 | PO2 | PO3 | PO4 | PO5 | PO6 | PO7 | PO8 | PO9 | PO10 | PO11 |
| MAH621B | DYNAMICS OF RIGID BODY | CO1 | To demonstrate that they can apply the concept of system of particle in finding moment of inertia, D’Alembert’s Principle and consequently knows the inertia constants for a rigid body and the equation of momental ellipsoid together with the idea of principal axes and principal moments of inertia. | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 |
| CO2 | To apply the concept of the dynamics involving a single particle like projectile motion, Simple harmonic motion, pendulum motion and related problems so that they can use these methods to solve real world problems. | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| CO3 | To demonstrate an ability to apply the concepts of motion of rigid body in two & three dimensions, system of Euler’s dynamical equations for studying rigid body motions for solving real world problems. | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| CO4 | To analyze the derivation of Lagrange’s Equations. Extension of Hamilton’s principle to non-holonomic systems. Distinguish the concept of the Hamilton Equations of motion and the Principle of Least Action. | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| MAH612B | COMPUTATIONAL FLUID DYNAMICS | CO1 | Demonstrate an ability to recognize the type of fluid flow that is occurring in a particular physical system and to use the appropriate model equations to investigate the flow. | 3 | 3 | 3 | 3 | – | – | 2 | 2 | 1 | 1 | 1 |
| CO2 | Demonstrate an ability to recognize the type of fluid flow that is occurring in a particular physical system and to use the appropriate model equations to investigate the flow. | 3 | 3 | 3 | 3 | – | – | 2 | 2 | 1 | 1 | 1 | ||
| CO3 | Demonstrate the ability to simplify a real fluid-flow system into a simplified model problem, to select the proper governing equations for the physics involved in the system, to solve for the flow, to investigate the fluid-flow behavior, and to understand the results. | 3 | 3 | 3 | 3 | – | 3 | 2 | 2 | 1 | 1 | 1 | ||
| CO4 | Demonstrate the ability to analyze a flow field to determine various quantities of interest, such as flow rates, heat fluxes, pressure drops, losses, etc., using flow visualization and analysis tools. | 3 | 3 | 3 | 3 | – | – | 2 | 2 | 1 | 1 | 1 | ||
| MAH613B | GENERALIZED FUZZY SET THEORY | CO1 | Explain the concept of advanced level of Generalized fuzzy set. | 3 | – | 1 | 2 | – | – | – | – | – | 1 | – |
| CO2 | Relate the concepts of soft sets, rough multisets. | 3 | – | 2 | 2 | – | – | – | – | – | 1 | – | ||
| CO3 | Apply structures such as Multisets, Rough sets. | 3 | 3 | 3 | 2 | – | – | 2 | – | 1 | 2 | – | ||
| CO4 | Solve and analyze real world problems using advanced level fuzzy techniques. | 3 | 3 | 3 | 3 | 1 | – | 2 | – | 2 | 2 | – | ||
| MAH624B | ADVANCED DISCRETE MATHEMATICS | CO1 | Conceptual understanding of Mathematical Logic: Propositional logic. | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 |
| CO2 | Analyse the minimizations of circuits by using Boolean identities and K-map. | 1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| CO3 | Construct and express logical arguments using grammar and to work in abstract or general term to increase the clarity and efficiency of analysis. |
1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| CO4 | Introduce the automata theory and finite set of machine to determine the decidability and intractability of computational problem |
1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| CO5 | Discuss Euler and Hamilton paths and circuits and Evaluate minimal spanning tree for the undirected graphs. |
1 | 2 | 3 | 2 | – | 1 | 2 | 2 | 3 | 3 | 1 | ||
| MAH618B | LIGHTLIKE MANIFOLDS | CO1 | Demonstrate the ability to aply the concepts of of metric tensor, isometries, curvature and geodesic of a semi-Riemannian manifolds to prove the theorem and mathematical problem based on these topics | 3 | – | 2 | 1 | – | – | – | – | 3 | – | 3 |
| CO2 | Explain connection, normal connection totally geodesic , hypersurfaces and solve related mathematical problems | 3 | – | 2 | 1 | – | – | – | – | 3 | – | 3 | ||
| CO3 | Apply the concept of lightlike hypersurfaces to rove results on screen conformal hypersurfaces, induced scalar curvature , Einstein hypersurface | 3 | – | 2 | 1 | – | – | – | – | 3 | – | 3 | ||
| CO4 | prove results on half lighlike submanifolds, screen conformal submanifolds | 3 | – | 2 | 1 | – | – | – | – | 3 | – | 3 | ||
| MAH616B | STOCHASTIC PROCESSES | CO1 | Illustrate and formulate fundamental probability distribution and density functions, as well as functions of random variables | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | – | – |
| CO2 | Analyze continuous and discrete-time random processes | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | ||
| CO3 | Apply the theory of stochastic processes to analyze linear systems | 1 | 2 | 2 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | ||
| CO4 | Apply the above knowledge to solve basic problems in filtering, prediction and smoothing | 1 | 2 | 2 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 2 | ||
| MAH617B | HARMONIC ANALYSIS | CO1 | Explain the concept of Haar measure and identify Haar measures for the group of the integers, the reals under addition and multiplication, the torus, and the ax+b group. | 3 | – | 3 | 2 | – | – | – | – | 3 | – | 3 |
| CO2 | Use the Gelfand-Naimark it to identify the C* algebra of the groups R_nand Z_n. | 3 | – | 3 | 2 | – | – | – | – | 3 | – | 3 | ||
| CO3 | Explain the concept of Pontryagin duality and the connection with the Fourier series and Fourier transform. | 3 | – | 3 | 2 | – | – | – | – | 3 | – | 3 | ||
| CO4 | Use the Pontryagin duality to identify duals of examples of locally compact abelian groups | 3 | – | 3 | 2 | – | – | – | – | 3 | – | 3 | ||
| MAH615B | CODING THEORY | CO1 | Demonstrate simple ideal statistical communication models. | 3 | – | 1 | 2 | – | – | – | – | – | 1 | – |
| CO2 | Explain the development of codes for transmission and detection of information. | 3 | – | 2 | 2 | – | – | – | – | – | 1 | – | ||
| CO3 | Utilize various error control encoding and decoding techniques | 3 | 3 | 2 | 2 | – | – | 2 | – | 1 | 2 | – | ||
| CO4 | Apply information theory and linear algebra in source coding and channel coding | 3 | 3 | 3 | 3 | 1 | – | 2 | – | 2 | 2 | – | ||
| CO5 | Analyze the performance of error control codes. | 3 | 3 | 3 | 3 | – | – | 2 | – | 2 | 2 | 1 | ||
| MAH619B | WAVELETS & IT’S APPLICATIONS | CO1 | Recognise the importance of discrete wavelet transform and MRA | 3 | 3 | 2 | 3 | 1 | 1 | 2 | 2 | 3 | 2 | 2 |
| CO2 | Analyse and construct alternative wavelet representations | 3 | 3 | 2 | 3 | 1 | 1 | 2 | 2 | 3 | 3 | 2 | ||
| CO3 | understand the fundamental concepts of wavelets which has applications in the development of tools and techniques which may be used in signal theory, image processing, communication techniques, graphical algorithms and numerical analysis. | 3 | 3 | 2 | 3 | 3 | 1 | 2 | 2 | 3 | 3 | 3 | ||
| CO4 | apply the concepts of theory of wavelets for solving problems in mathematics, signal & image processing. | 3 | 3 | 2 | 3 | 3 | 1 | 2 | 2 | 3 | 3 | 3 | ||
| MAH620B | ALGEBRAIC TOPOLOGY | CO1 | Explain the fundamental concepts of algebraic topology and their role in modern mathematics and applied contexts. | 3 | – | 3 | 2 | – | – | – | – | 3 | – | 3 |
| CO2 | Demonstrate accurate and efficient use of algebraic topology techniques. | 3 | – | 3 | 2 | – | – | – | – | 3 | – | 3 | ||
| CO3 | Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from algebraic topology. | 3 | – | 3 | 2 | – | – | – | – | 3 | – | 3 | ||
| CO4 | Apply problem-solving using algebraic topology techniques applied to diverse situations in physics, engineering and other mathematical contexts. | 3 | – | 3 | 2 | – | – | – | – | 3 | – | 3 | ||
| MAH626B | Project | CO1 | Understand the basic concepts & broad principles of research projects | 3 | 2 | 3 | 1 | 2 | 2 | – | – | 3 | 2 | – |
| CO2 | Get capable of self education and clearly understand the value of achieving perfection in project implementation & completion. | 3 | 3 | 3 | 2 | 3 | – | – | – | 3 | 2 | 1 | ||
| CO3 | Apply the theoretical concepts to solve problems with teamwork and multidisciplinary approach. | 3 | 2 | 3 | 2 | 2 | – | 2 | 3 | 3 | 3 | 2 | ||
| CO4 | Demonstrate professionalism with ethics; present effective communication skills and relate issues to broader societal context. | – | – | – | – | – | 3 | 2 | 3 | – | 2 | 2 | ||
| Total | 109 | 71 | 115 | 92 | 23 | 25 | 52 | 44 | 103 | 68 | 69 | |||
Program Structure
Scheme & Syllabus
The programme follows the choice-based credit system. The total credit requirement for the award of the M.Sc Mathematics degree is 82 depending upon the specified curriculum and scheme of examination of M.Sc Mathematics program. The distribution of credits over the semesters of the programme is as specified in the table below:
| S.No. | Semester | Classroom Contact Hours | Non-Teaching
Outcome Hrs |
Credits | |
| 1 | First Semester | 22 | 0 | 19 | |
| 2 | Second Semester | 22 | 4 | 24 | |
| 3 | Third Semester | 21 | 4 | 22 | |
| 4 | Fourth Semester | 10 | 12 | 18 | |
| Total Credits For M.Sc. Mathematics Programme | 75 | 30 | 83 | ||
Student shall also pass all University mandatory courses, audit courses, life skill program series points and shall fulfill any other requirement as prescribed by the University from time to time.
Career Opportunities:
- Teaching and Research
- IT Industry Banking Sector
- UPSC
- Civil Services
- Indian Railways
- Technical Writing
- Computer System Analyst
- Data Analyst
- Teaching at School and University level
