HomeProgrammes

Programmes Offered

  • B.Sc. (Hons)
  • M.Sc. Mathematics
  • M.Sc. Mathematics with Specialization in Computer Applications
  • M. Phil.
  • P. G. Diploma in Big Data, Logistics & Operations Research
  • Ph. D.

Syllabus

Programme Specific Outcomes

 

 

B. Sc. Mathematics Honors

PSO 1. Builds a firm foundation and provides a sound understanding of the basic principles of Mathematics, essential for a right appreciation of applied and advance Mathematics courses as well as other disciplines.

 

PSO 2. Prepare students to think and reflect statistically.

 

PSO 3. Provide experience of solving mathematical problems using computer softwares and programming.

 

PSO 4.Train students to master relevant definitions, examples, basic results and their proofs.

 

PSO 5. Develops logical thinking and enhance reading, writing and communication abilities.

 

PSO 6. Teaches perseverance and tolerance and inculcates moral and ethical values.

M. Sc. Mathematics

Besides offering courses in various areas of Pure and Applied Mathematics, this programme is well blended with computer programming & Statistics courses and also provides an experience of short-term research activity. The objective is to prepare students as responsible persons endowed with moral and ethical values, who have sound mathematical understanding, who can realize the relevance of the subject in the present day context and who have the capability of original thinking and original writing. After the completion, students have a wide variety of options as they can adopt research as a career or take up teaching jobs or can get employment in software industry or can go for any other profession.

M. Sc. Mathematics with Specialization in Computer Applications

The M.Sc. Mathematics with Specialization in Computer Applications has been designed with the objective of producing post graduates who are ready for employment in the Software Industry. With a strong background in Mathematics, niche areas in the software industry involving modelling, optimization and the application of mathematical techniques would also be accessible to the students. Students are thus expected to be proficient in areas of applied mathematics and software development.

M. Phil.

It is a two term short intermediate programme between M.Sc. and Ph. D. providing further training in core mathematical disciplines and research. Besides two theory courses, a self-study course and dissertation are the main components of this programme which make students become self dependent by acquiring mathematical maturity.

 

Post Graduate Diploma in Big Data, Logistics and Operations Research (PGDBDLOR)

It is a two semester programme and its duration is one year. The objective of this programme is to provide a strong foundation in Statistics, Analytics, Information Systems and Operations Research for effective decision making and building systems based on considerations of data, mining, risk, prescriptive and predictive analysis and the application of decision tools and techniques.

 

Course Outcomes

B.Sc. Mathematics

 

Course Code

                         Courses Title

Course Outcome

Semester I

 

 

MAM 101

Statistics I

Course Content: Measures of central tendency, Basics of probability, Random variables and their properties, Discrete and continuous probability distributions and their properties

This course

1. Inculcates basic concepts of statistics.

2. Develops the ability to analyse the given data.

3. Develops thinking of real life problems in statistical environment.

4. Prepares them to attend the statistical part of competitive exams after graduation.

MAM 102

Discrete Mathematics

Course Content:Mathematical Logic, Set Theory, Combinatorics, Recurrence relations and Generating functions. Main emphasis has been given to the basic of discrete mathematics and its applications.

This course helps the students to

1.      Develop an understanding of abstract notions.

2.      Develop an appreciation of mathematical abstraction and generalization.

3.      Write elementary proofs on their own.

4.      Enhance their reasoning capability and logical thinking.

5.      Bring in their creativity.

MAM103

Seminar & Group Discussion

Course Content:Presentations in the class by the student, on topics related to the courses studied in that semester.

This course will help the students to

1. Overcome hesitation of public speech.

2. Learn communication of mathematical ideas.

3. Learn and improve their presentation skills using chalk and duster.

4. Interact with class mates and course teacher.

5. Learn to express their thoughts in public.

MAW101

Computer Aided Statistical Tech. I

Course Content: Introduction to MATLAB commands and basic programming in MATLAB.

This course will help the students to

1. Get hands on experience of working with computers.

2. Learn in-built functions of MATLAB as quick and ready to use tools in programming.

3. Learn to solve graphical problems using MATLAB.

Semester II

 

 

MAM201

Analysis I (Calculus of One Variable)

Course Content:Real Number System and Completeness Property, Archemedian Prorerty, Rational  Density Theorem, Convergence of  Sequence and Series,Derivative of a Real Function, Intermediate Value Theorem, Extreme Value Theorem. Indeterminate Forms, Applications of Derivatives, Polar Curves.

Major theorems are proved.  Related examples are facilitated for sound understanding of the subject.

This course helps the students to

1. Understand, read and write mathematics.

2. Understand and write proofs.

3. Write elementary proofs on their own.

4. Enhance their reasoning capability and logical thinking.

5. Visualize mathematical notions geometrically.

MAM202

Algebra I (Groups & Rings)

Course Content:Group, ring and field and related results.

This is the first exposure to abstract mathematics. Examples are central to the course and facilitate sound understanding of the abstract notions. Mathematical rigour is nowhere diluted.

This course will help the students to

1. Develop an understanding of abstract notions.

2. Learn the fundamentals of Abstract Algebra.

3. Write elementary proofs on their own.

4. Enhance their reasoning capability and logical thinking.

MAM203

Seminar & Group Discussion

Course Content:Presentation in the class by the student of a topic related to the courses studied in that semester.

This course will help the students to

1. Overcome hesitation of public speech.

2. Learn communication of mathematical ideas.

3. Improve their presentation skills using chalk and duster.

4. Interact with class mates and course teacher.

5. Learn to express their thoughts in public.

MAW 201

Computer Aided Statistical Tech. II 

Course Content: Advanced MATLABprogramming.

This course will help the students to

1. Get hands on experience of working with computers.

2. Learn to solve arithmetic problems.

3. Solve problems of numerical analysis.

Semester III

 

 

MAM 301

Analysis II (Integration & Convergence)

Course Content: This course covers the basic properties and techniques of integration of real valued functions of one variable and its application to finding area, volume, surface area etc. The course also deals with the uniform convergence of the sequence and series of functions with emphasis on power series and elementary transcendental functions.

Examples are central to the course and facilitate sound understanding of the abstract notions. Course is carried out with full mathematical rigour with lots of examples.

This course helps the students to

1.      Develop an understanding of the fundamental concepts behind the integration and its application.

2.      Understand the notion of uniform convergence and its consequences.

3.      Solve problems pertaining to sequence and series of functions.

 

MAM 302

Algebra II (Linear Algebra)

Main topics discussed are vector spaces ,basis and dimensions, linear transformations, rank, elementary matrices,  similarity, determinants, theory of system of linear equations, eigenvalues, eigenvectors and diagonalization.

This course helps the students to

1. Gain an insight into the abstract mathematical systems of linear algebra.

2. Understand the importance of vector spaces.

MAM 303

Operations Research

Course Content:L.P.P and its geometry, Post optimality analysis, Transportation problem, Assignment problem, Travelling salesman problem, Game theory, Inventory theory.

This course helps the students to

1.      Understand the importance and significance of operations research.

2.      Develop an understanding of geometry of L.P.P.

3.      Understand proofs related to the structure of solution set of L.P.P.

4.      Understand the importance of post optimality analysis.

5.      Understand applications of L.P.P in transportation and assignment problems.

6.      Understand game theoretic concepts.

7.      Learn the importance of queueing theory and its various models.

MAM 304

Seminar & Group Discussion

Course Content:Presentations in the class by the student, on topics related to the courses studied in that semester.

This course will help the students to

1. Overcome hesitation of public speech.

2. Learn communication of mathematical ideas.

3. Learn and improve their presentation skills.

4. Interact with class mates and course teacher.

5. Learn to express their thoughts in public.

Semester IV

 

 

MAM 401

Differential Equations I (Ordinary Differential Equations)

Course Content:Equations of first order and first degree, Linear equations with constant coefficients, simultaneous equations, total differential equations, Solution in series, Bessel’s equation, Legendre’s equation, Hypergeometric equation, Laguerre equation, Hermite equation.

 

This course helps the students to

1.      Develop an understanding of ODEs.

2.      Understand methods of solutions of different types of ODEs.

3.      Understand methods to obtain solution of ODEs in series.

4.      Learn Bessels, Legendres, Hypergeometric, Laguerre and Hermite equations.

5.      Understand their recurrence relations, orthogonality and solution methods.

6.      Understanding polynomials associated with solution of such equations.

 

 

 

 

MAM 402

Statistics II

Course Content: Marginal and joint probability distributions, Correlation and Regression, Central limit Theorem, Sampling and sampling distributions, Hypothesis testing

This Course

1. Develops critical thinking.

2. Prepares students to apply statistical techniques in social and environmental problems.

3. Prepares students to use statistical techniques in research in future.

4. Provides an opportunity to do the projects on various social issues.

5. Inculcates ethics in the personality of the students as this course is itself based on ethics.

6. Creates ability to engage in independent and lifelong learning which caters to socio-technological changes.

7. Prepares students to face the problems on statistics in competitive exams.

MAM 403

Analysis III (Vector Calculus)

Course Content:This course  includes the limit, continuity, differentiation of maps from Rn to Rm and related results. Multiple integrals, line and surface integrals are introduced followed by their applications and related theorems.

Course is carried out with full mathematical rigour with lots of examples. Surfaces and curves are explained using 3-D graphs generated by MATLAB.

This course helps the students to

1.       Get equipped at a level of proving inverse function and implicit function theorems.

2.       Visualize surfaces & curves

3.       Understand the meaning of integrating over a surface and over a curve.

4.       Solve problems concerned with surface and line integrals.

MAM 404

Seminar & Group Discussion

Course Content:Presentations in the class by the student, on topics related to the courses studied in that semester.

This course will help the students to

1. Overcome hesitation of public speech.

2. Learn communication of mathematical ideas.

3. Learn and improve their presentation skills.

4. Interact with class mates and course teacher.

5. Learn to express their thoughts in public.

Semester V

 

 

MAM 501

Metric Spaces

Course Content:This course introduces Metric spaces with main focus on open sets, convergence of sequences, continuity, compactness and completeness.   Important theorems such as Category theorem, Cantor intersection theorem, inverse and implicit theorems are also proved with an emphasis on their applications.

All the terms and notions are explained using examples which facilitate sound understanding of the abstract notions.

This course helps the students to

1. Develop an understandingof abstract notions.

2. Understand, read and write mathematics.

3. Write elementary proofs on their own.

4. Enhance their reasoning capability and logical thinking.

MAM 502

Curves & Surfaces

Course Content:Curvature of curves in 3-dimensional Euclidean space, geodesics and mean and Gaussian curvature of 2-dimensional surfaces.

Course is carried out with full mathematical rigour with lots of examples. This course will help the students to

1. Visualize mathematical notions geometrically.

2. Understand, read and write mathematics.

3. Solve problems on their own.

4. Enhance their reasoning capability and logical thinking.

 

MAM 503

Differential Equations II (Partial Differential Equations)

Course Content:Solutions of first order PDEs, Canonical Forms, Hyperbolic, Parabolic and Elliptic Equations.

This course helps the students to

1.      Develop an understanding of abstract notions.

2.      Develop an appreciation of mathematical abstraction and generalization.

3.      Understand and write proofs.

4.      Write elementary proofs on their own.

5.      Enhance their reasoning capability and logical thinking.

6.      Visualize mathematical notions geometrically.

7.      Solve new problems.

MAM 504

'C' & Data Structures

This course covers programming fundamentals, the complete C Programming Language, analysis of algorithms and the following important data structures: arrays, stacks, 1ueues, sequential and linked implementations, binary trees, binary search trees, hash tables; and searching and sorting.

Students are expected to,

1. Understand, formulate and analyse algorithms

2. Code algorithms in the C language

3. Be proficient in applying advanced concepts such as pointers and recursion in C

4. Use various libraries in C

4. Develop an understanding of data structures from mathematical abstractions to implementation in C

5. Understand the application of a data structure through concrete examples.

6. Code applications of data structures.

 

MAM 505

Algebra III (Sylow’s Theorems & Inner Product Spaces)

Course Content: Main Topics-- Cauchy’s theorems, Sylow’s theorems, Index theorem, Quaternion group, Dihedral group, Classification of groups, Inner product spaces, orthogonal sets, Orthogonalization process, Linear operator, Adjoint and Orthogonal operators, Positive definite operators

This course helps the student to

1.      Study the symmetric structures through group theoretic approach

2.      Use hessian matrix in developing optimization techniques

3.      Understand applications of group theory

4.      Understand important concepts and methodologies used by physicists, Chemists, computer scientists and mathematicians.

MAM 506

Programming Lab

Course Content: C programming language, problems based on the course                             MAM 504- C and data Structures

In this course students are expected to implement algorithms in C and expected to implement all data structures taught in course MAM504 along with their specific applications. After the course they are expected to gain proficiency in formulating and implementing algorithms in C and view and implement data structures from an application perspective.

 

 

Semester VI

 

 

MAM 601

Number Theory

Course Content:Main topics- Number Theoretic functions, Chinese Remainder theorem, Fermat’s Little theorem, Wilson Theorem, Euler’s theorem, Primitive roots, Quadratic residues, Continued Fractions.

Major theorems with their proofs and applications are discussed.  Examples are central to the course and facilitate sound understanding of the abstract notions.

This course helps the students to

1. Develop an understanding of abstract notions.

2. Develop an appreciation of mathematical abstraction and generalization.

3. Understand and write proofs.

4. Enhance their reasoning capability and logical thinking.

MAM 602

Complex Analysis 

Course Content:Analytic Functions, Cauchy-Goursat's Theorem, Liouville’s Theorem, Fundamental Theorem of Algebra, Maximum Modulus Theorem, Taylor’s Theorem, Laurent’s Theorem, Cauchy’s Residue Theorem,Complex Integration and Möbius Transformations.

Major theorems with their proofs, related examples and applications are discussed.  Course is carried out with full mathematical rigour.

This course helps the students to

1. Understand and write proofs.

2. Enhance their reasoning capability and logical thinking.

3. Visualize mathematical notions geometrically.

4. Solve problems using new techniques.

MAM 603

Methods of Applied Mathematics

Course Content: Laplace transform, Inverse Laplace transform, Fourier series, Applications, Solution of heat conduction and wave equations, Integral equations, Eigen function of integral equations

This course helps the students to

1.      Solve physical and mechanical problems governed by differential equation and integral equation.

2.      Understand conversion of differential equation into integral equation.

3.       Understand conversion of partial differential equations into ordinary differential equations.

4.      Understand applications of eigen values and eigen vectors in physical problems.

5.      Understand application of proper and improper integrals in physical problems.

 

MAM 604

Numerical Analysis

  1. Solution of nonlinear equations, Order of convergence.
  2. Direct and iterative methods  for  solution of Linear Systems.
  3. Interpolation.
  4. Numerical  Differential and Integration. Condition Number, Power method, House holder matrix

The QR method.

  1. Numerical solution of Ordinary Differential Equations, their stability. Multistep methods.Finite difference schemes for solving partial differential equations.

This course develops understanding of fundamentals of numerical methods.

 

MAM 605

Tensor Analysis

Course Content:The course deals with the notion of tensors on vector spaces and hence on tangent spaces at a point on the surface.

This course demonstrates

1.      Presentation of equations in physics in a form that is independentof the choice of coordinates.

2.      Methods so that complicated equations become easy to handle with the help of tensor notation.

MAM 606

Programming Lab

This course covers the MATLAB package and programming in MATLAB. Students have to implement algorithms in Numerical Analysis. After the course students are expected to know all the basic commands in MATLAB, be able to work with specific tool boxes and be able to use the MATLAB programming language for coding algorithms in mathematics and for effective visualization.

 

 

M.Sc. Mathematics

 

          Course Code

           Courses Title

 

Term I

 

 

MAM701

Measure &  Integration

Course Content: This course is concerned with the Lebesgue measure and Lebesgue  integration for the functions of a real variable. Lp spaces are also introduced.

The course provides an opportunity to encounter new concepts in a familiar setting, which provides a foundation and motivation for the more abstract concepts. Establishing inequalities in Lp spaces provides another important example of a metric space.

This course helps the students to

Develop an appreciation of mathematical abstraction and generalization.

MAM702

Topology

Course Content:Topological Space, metric topology, homeomorphism, topological properties namely separation axioms, compactness, connectedness and compactness. This is the first course on Topology. Course is carried out with full mathematical rigour with lots of examples.

 

This course will help the students to

1. Develop an appreciation of mathematical abstraction and generalization.

2. Learn classification of topological spaces

3. Visualize mathematical notions geometrically.

4. Understand, read and write mathematics.

5. Enhance their reasoning capability and logical thinking.

6. Bring in their creativity.

7. Learn how to mathematically model and define a geometric property.

 

MAM703

Theory of Differential Equations

1. Lipschitz condition, Gronwall inequality, Existence and uniqueness of solutions.

2. Concept of Wronskian. Oscillatory and non-oscillatory equations. Strum -Liouville boundary Value Problem, Green’s  function.

3. Fundamental matrix. Linear systems with constants, Linear Systems with Periodic coefficients.

4. Stability of Linear Systems.

5. Stability of Nonlinear Differential Equations, Application of Poincare Bendixson Theorem.

6. Methods of solution of integral equations.

7. This course concerns with fundamentals of Differential Equations.

 

MAM704

Analytical Mechanics

Course Content: Lagrange’s, Hamilton’s, Hamilton-Jacobi, Euler’s equations of a dynamical system; Hamilton’s principle, Principle of least action, Equilibrium configuration, Small oscillations, Least action, Liouville’s theorem, Phase space, Poisson bracket, Variational methods

This course helps the student to

1.      Learn mathematical modelling of dynamical systems

2.      Search equilibrium (stable/unstable) configuration of dynamical systems.

3.      Learn classical mechanics as a background for quantum mechanics.

4.      Learn Hamiltonian theory used in engineering studies.

MAM705

Rings & Canonical Forms

Course Content:Polynomial rings, irreducibility of polynomials, quadratic integer rings, Euclidean, principal ideal and unique factorization domains, minimal polynomial, diagonalizability and triangulability of matrices and linear operators, Jordan and rational canonical forms.

 

This course helps the students to

1. Learn some advanced topics in Abstract Algebra.

2.  Appreciate and command proofs.

3. Enhance their reasoning capability and logical thinking.

 

MAM706

Software Lab

This course covers the JAVA programming language and MATLAB.

After this course students are expected to be able to understand and implement the object-oriented paradigm, inheritance, exception handling, interfaces, packages, enumerations, file i/o, understand to read the Java Documentation and use some of the important Java packages. Students are also expected to learn and implement algorithms in MATLAB.

 

Term  II

 

 

MAM801

Optimization

Course Content:Queueing Theory, Non-Linear Programming Problem, Unconstrained and constrained optimization, Dynamic Programming, Integer programming.

 

This course helps the students to

1.      Develop an understanding of queueing models and their applications.

2.      Understand concave and convex functions, quadratic forms.

3.      Learn methods for nonlinear unconstrained optimization problems.

4.      Learn methods for nonlinear constrained optimization problems.

5.      Develop understanding of multi stage optimization (dynamic programming problem).

6.      Learn methods to solve pure and mixed IPPs.

MAM802

Field Theory                               

Course Content:Main topics-Field extensions, finite fields, solvable groups and solvability of polynomials. Major theorems with their proofs and applications are discussed.  Examples are central to the course and facilitate sound understanding of the abstract notions.

This course helps the students to

1. Develop an appreciation of mathematical abstraction and generalization by studying various applications.

2.  Appreciate and command proofs.

3. Understand, read and write mathematics.

4. Enhance their reasoning capability and logical thinking.

MAM 803

Functional Analysis

Course Content: In this course normed linear spaces and Hilbert spaces are introduced. The course familiarizes the student with the basic concepts, principles and methods of functional analysis and its applications. Spectral theorem for finite dimensional spaces is another important feature of this course. Major theorems with their proofs and applications are discussed.  Examples facilitate sound understanding of the abstract notions. Mathematical rigour is nowhere diluted.

This course helps the students to

1. Understand and write proofs.

2. Enhance their reasoning capability and logical thinking.

MAM804

Fluid Dynamics

1.      Basics of kinematics and fluid dynamics.

2.      Students will be able to understand and solve various industrial problems related to fluid flow.

3.      Problems of Bio-fluid dynamics.

4.      Non-dimensional analysis to be used in various research problems.

MAM805

Stochastic Proc. & Stat. Inference

In this course many phenomenon occurring in physical and life sciences, social sciences, engineering and management are studied not only as random but as stochastic processes, i.e changing with time and space. The course also covers theory of estimation, hypothesis testing, reliability theory and design of experiments.

MAM806

Software Lab         

It enables students to implement and run algorithms taught in the theory courses and use it on different problems. The package used is MATLAB. For Pure Mathematics Specialization this course supports theory courses run in the same semester.

 

MAM812

Graph Theory

This course covers basic concepts in undirected graphs and directed graphs, classes of graphs such as Euler Graphs and Hamiltonian Graphs, trees, graph connectivity and network flows, graph colouring, graph matching, planar graphs and graph alogorithms covering traversals, spanning trees, shortest paths and maximum matching.

Students are expected to

1. Gain a rigorous understanding of a graph and its terminology.

2. Understand various proof strategies.

3. State all of the relevant theorems.

4. Learn to model problems using graphs and to solve these problems algorithmically.

Term III(Summer Term)

MAM001

Research Methodology

Course Content: Introduction to various methods involved in research e.g. synopsis preparation, statistical analysis of the results and report writing.

This course

1.      Provides motivation for research.

2.      Prepares a student for research activities.

MAM002

Pre-Dissertation

Course Content:A synopsis is prepared by the student under the supervision of a teacher, outlining the work one is supposed to carry out in one semester. It is a first exposure to research.

This course

1. Implants the seeds for original thinking and original writing.

2. Teaches formal mathematical writing of research level.

3. Develops presentation skills using power point.

4. Develops aptitude for research.

5. Gives exposure of current research papers and research journals.

Term IV

 

 

MAM901

Dissertation

Course Content:The student carries out the work under the supervision of a teacher, as proposed in MAM 002 and submits a report at the end of the semester. It is a short span research activity.

This course

1. Inculcates creativity, original thinking and skills for original writing.

2. Teaches formal mathematical writing of research level.

3. Develops presentation skills using power point.

4. Develops aptitude for research.

5. Gives exposure of current research papers and research journals.

6. Imparts confidence in students to solve new problems.

MAM 902

Mathematical Modelling

This course deals with some aspects of population dynamics, mathematical epidemiology, mathematical genetics, pollution control and optimization models in biology and medicine besides the basic concepts of mathematical modelling. The new frontiers of mathematics are the domains of biology and medicine. The gradual invasion of these fields by mathematicians is already yielding a number of benefits as a result of the application of known techniques along with digital computers.

MAM 903

Introduction to Riemannian Geometry

Course Content:Topological manifolds, differentiable manifolds, differentiable functions on manifolds, tangent spaces, vector fields, differentiation of vector fields, geodesics, linear connection, covariant derivate, Riemannian curvature tensor.

 

This course deals with the basics of differentiable manifolds, a notion that is a prerequisite for advance research in Mathematics and some of the other disciplines also, leading to the fundamentals of Riemannian Geometry.

MAM 904

Fuzzy Sets & Systems

Course Content:Fuzzy sets their operations and properties, fuzzy arithmetic, fuzzy relations, fuzzy logic, fuzzy controllers, defuzzification methods.

                                                                                                                                                                       

This course helps the students to

1.      Learn importance of fuzzy sets over classical sets.

2.      Understand concept of membership.

3.      Understand operators and properties of fuzzy sets.

4.      Develop applications of fuzzy sets in real life.

5.      Understand importance of fuzzy logic over classical logic.

6.      Learn design of fuzzy experts systems.

7.      Understand applications of fuzzy controllers.

8.      Learn various fuzzification and defuzzification methods.

       

 

 

M.Sc. Mathematics with Specialization in Computer Applications

 

          Course Code

           Courses Title

 

Term I

 

 

MAM701

Measure &  Integration

Course Content: This course is concerned with the Lebesgue measure and Lebesgue integration for the functions of a real variable. Lp spaces are also introduced.

The course provides an opportunity to encounter new concepts in a familiar setting, which provides a foundation and motivation for the more abstract concepts. Establishing inequalities in Lp spaces provides another important example of a metric space.

This course helps the students to

Develop an appreciation of mathematical abstraction and generalization.

MAM702

Topology

Course Content: Topological Space, metric topology, homeomorphism, topological properties namely separation axioms, compactness, connectedness and compactness. This is the first course on Topology. Course is carried out with full mathematical rigour with lots of examples.

 

This course will help the students to

1. Develop an appreciation of mathematical abstraction and generalization.

2. Learn classification of variuos topological spaces

3. Visualize mathematical notions geometrically.

4. Understand, read and write mathematics.

5. Enhance their reasoning capability and logical thinking.

6. Bring in their creativity.

7. Learn how to mathematically model and define a geometric property.

 

MAM703

Theory of Differential Equations

1. Lipschitz condition, Gronwall inequality, Existence and uniqueness of solutions.

2. Concept of Wronskian. Oscillatory and non-oscillatory equations. Strum -Liouville boundary Value Problem, Green’s  function.

3. Fundamental matrix. Linear systems with constants, Linear Systems with Periodic coefficients.

4. Stability of Linear Systems.

5. Stability of Nonlinear Differential Equations, Application of Poincare Bendixson Theorem.

6. Methods of solution of integral equations.

This course concerns with fundamentals of Differential Equations.

 

MAM706

Software Lab

This course covers the JAVA programming language and MATLAB.

After this course students are expected to be able to understand and implement the object-oriented paradigm, inheritance, exception handling, interfaces, packages, enumerations, file i/o, understand to read the Java Documentation and use some of the important Java packages. Students are also expected to learn and implement algorithms in MATLAB.

 

MAM707

Computer Systems Architecture

Same as CSM 503

MAM 708

Database Management Systems

Same as CSM 303

Term  II

 

 

MAM801

Optimization

Course Content:Queueing Theory, Non-Linear Programming Problem, Unconstrained and constrained optimization, Dynamic Programming, Integer programming.

 

This course helps the students to

1.      Develop an understanding of queueing models and their applications.

2.      Understand concave and convex functions, quadratic forms.

3.      Learn methods for nonlinear unconstrained optimization problems.

4.      Learn methods for nonlinear constrained optimization problems.

5.      Develop understanding of multi stage optimization (dynamic programming problem).

6.      Learn methods to solve pure and mixed IPPs.

MAM805

Stochastic Proc. & Stat. Inference

In this course many phenomenon occurring in physical and life sciences, social sciences, engineering and management are studied not only as random but as stochastic processes, i.e changing with time and space. The course also covers theory of estimation, hypothesis testing, reliability theory and design of experiments.

MAM806

Software Lab    

It enables students to implement and run algorithms taught in the theory courses and use it on different problems. The package used is MATLAB. For Pure Mathematics Specialization this course supports theory courses run in the same semester.

 

MAM 807

Internet Technologies

Same asCSM401

MAM 808

Software Engineering

Same asCSM601

MAM 809

Cryptography & Security

Same asCSM603

MAM 810

Intelligent Information Processing(same as PHM 960)

Same asCSM802

MAM 811

Advanced Algorithms

Same asCSM 951

MAM812

Graph Theory

This course covers basic concepts in undirected graphs and directed graphs, classes of graphs such as Euler Graphs and Hamiltonian Graphs, trees, graph connectivity and network flows, graph colouring, graph matching, planar graphs and graph algorithms covering traversals, spanning trees, shortest paths and maximum matching.

Students are expected to

1. Gain a rigorous understanding of a graph and its terminology.

2. Understand various proof strategies.

3. State all of the relevant theorems.

4. Learn to model problems using graphs and to solve these problems algorithmically.

Term III(Summer Term)

 

 

MAM001

Research Methodology

Course Content: Introduction to various methods involved in research e.g. synopsis preparation, statistical analysis of the results and report writing.

This course

1.      Provides motivation for research.

2.      Prepares a student for research activities.

MAM002

Pre-Dissertation

Course Content:A synopsis is prepared by the student under the supervision of a teacher, outlining the work one is supposed to carry out in one semester. It is a first exposure to research.

This course

1. Implants the seeds for original thinking and original writing.

2. Teaches formal mathematical writing of research level.

3. Develops presentation skills using power point.

4. Develops aptitude for research.

5. Gives exposure of current research papers and research journals.

Term IV

 

 

MAM901

Dissertation

Course Content:The student carries out the work under the supervision of a teacher, as proposed in MAM 002 and submits a report at the end of the semester. It is a short span research activity.

This course

1. Inculcates creativity, original thinking and skills for original writing.

2. Teaches formal mathematical writing of research level.

3. Develops presentation skills using power point.

4. Develops aptitude for research.

5. Gives exposure of current research papers and research journals.

6. Imparts confidence in students to solve new problems.

MAM 904

Fuzzy Sets & Systems

Course Content:Fuzzy sets their operations and properties, fuzzy arithmetic, fuzzy relations, fuzzy logic, fuzzy controllers, defuzzification methods.

                                                                                                                                                                       

This course helps the students to

1.      Learn importance of fuzzy sets over classical sets.

2.      Understand concept of membership.

3.      Understand operators and properties of fuzzy sets.

4.      Develop applications of fuzzy sets in real life.

5.      Understand importance of fuzzy logic over classical logic.

6.      Learn design of fuzzy experts systems.

7.      Understand applications of fuzzy controllers.

8.      Learn various fuzzification and defuzzification methods.

MAM704

Analytical Mechanics

Course Content: Lagrange’s, Hamilton’s, Hamilton-Jacobi, Euler’s equations of a dynamical system; Hamilton’s principle, Principle of least action, Equilibrium configuration, Small oscillations, Least action, Liouville’s theorem, Phase space, Poisson bracket, Variational methods

This course helps the student to

1.      Learn mathematical modelling of dynamical systems

2.      Search equilibrium (stable/unstable) configuration of dynamical systems.

3.      Learn classical mechanics as a background for quantum mechanics.

4.      Learn Hamiltonian theory used in engineering studies.

MAM905

Computer Networks

Same asCSM502

MAM906

Computer Graphics

Same asCSM501

MAM907

Automata Theory & Formal Languages

Same asCSM701

M.Phil. Mathematics

Course Code

Course Title

 

Term I

MAM 951

Dissertation I

Course Content:A synopsis is prepared by the student under the supervision of a teacher, outlining the work one is supposed to carry out in the next term. Evaluation is done on the basis of write-up, regular presentations followed by rigorous discussions.

presentations followed by rigorous discussions.

This course

1. Strengthens original thinking and original writing.

2. Teaches formal mathematical writing of research level.

3. Develops presentation skills using power point.

4. Develops aptitude for research.

5. Gives exposure of current research papers and research journals.

MAM 953

Self Study Course

Course Content:Each student studies various topics of one’s choice under the supervision of a teacher and submits write-ups regularly. Evaluation is done on the basis of regular presentations followed by rigorous discussions.

 This course

1. Is a step towards making students to be self dependent.

2. Inculcates in students habit of reading books on their own.

3. Enhances presentation skills of students

 

MAM 954

Scientific Computing

Same as PHM 954

MAM 955

Special Topics in Mathematics

Course Content:Schur’s theorem, diagonalizability of self-adjoint operators, Bilinear and quadratic forms, orthogonal transformations & matrices, topological properties of matrix groups and PDEs of second order.

This course covers topics which use the knowledge of various courses previously studied and train the students in acquiring mathematical maturity and gaining insight into advance mathematical notions.

Term II

MAM 952

Dissertation II

Course Content:The student carries out the work under the supervision of a teacher, as proposed in MAM 951 and submits a report at the end of the semester. It is a short span research activity.

This course

1. Inculcates creativity, original thinking and skills for original writing.

2. Teaches formal mathematical writing of research level.

3. Develops presentation skills using power point.

4. Develops aptitude for research.

5. Gives exposure of current research papers and research journals.

6. Imparts confidence in students to solve new problems.

Post Graduate Diploma in Big Data, Logistics and Operations Research (PGDBDLOR)

 

Code

Title

Course Outcomes

 

Semester I

 

DBD 101

Basic Statistics

This course covers several key statistical techniques for analysing data, probability distributions and estimation and testing of hypothesis. It also provides an overview of modelling techniques such as correlation and regression analysis.

DBD 102

Operations Research

This course serves as an introduction to the field of Operations Research (OR). The course will cover linear programming in detail and its different applications. The course will also introduce the idea of Game Theory which is applicable to bargaining and negotiation and to Inventory Management.

DBD 103

Data Mining

This course is concerned with finding interesting and useful patterns in data repositories. It aims to provide knowledge on concepts, principles and techniques of data mining. It will also introduce some open source tools for analysing data.

DBD 104

Data Management, Visualization and R

This course will provide an introduction to databases and data visualization. The students will be able to design relational database schemas for various applications, load, transform, and query relational data and use techniques to visualize data with R. The students will also learn the R package and R programming and be able to use these in different applications for data cleaning and analytics.

DBD 105

Machine Intelligence

This course introduces several fundamental concepts and methods for machine learning. The objective is to familiarize the audience with some basic learning algorithms and techniques and their applications, as well as general questions related to analyzing and handling large data sets.

DBD 106

Computer Laboratory

To provide hands on experience on tools required for topics in Statistics, Operations Research, Data Management and Machine Intelligence.

 

 

 

Semester II

 

DBD 201

Stochastic Processes and Statistical Inference

In this course many phenomenon occurring in physical and life sciences, social sciences, engineering and management are studied not only as random but as stochastic processes, i.e changing with time and space. The course also covers theory of estimation, hypothesis testing, reliability theory and design of experiments.

DBD 202

Advanced Optimization Techniques

This course will cover advanced topics in operations research and optimization, namely, queueing theory, unconstrained and constrained non-linear programming, dynamic programming and integer programming.

DBD 203

Modelling and Simulation

The goal is to introduce students to basic simulation methods and tools for modelling and simulation of different types of systems.

DBD 204

Big Data Analytics

This course will cover the basic concepts of big data and methodologies for analyzing structured and unstructured data. It will introduce and cover the HADOOP ecosystem and also look at specific application domains for analytics.

DBD 205

Logistics, Social Media, Web and Learning Analytics

This course will cover topics in supply chain management, forecasting and Analytics in Social Media, Web and Learning. The course will cover all the essential concepts and current state of analytics in the above application domains. It will also introduce the idea of maturity models and analytics frameworks as applicable to the above domains.

DBD 206

Project

The students are expected to implement the analytics process in the context of some application.

DBD 001

Summer Project

This is an hands-on analytics training in some industry and institution.

 

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