The aim of the course is to introduce the fundamental areas of Algebra namely group theory and Ring theory to the students. This course will provide a strong foundations in the abstract approach for the budding mathematician. The course deals with the group Theory, Ting Theory and various standard results in these areas. One of the amazing features of twentieth century mathematics has been its recognition of the power of abstract approach. Modern algebra has evolved with this abstract approach, and is one of the important current research area of mathematics, and also serves as the unifying thread which interfaces all of mathematics – geometry, number theory, analysis, topology and even applied mathematics. The basic ideas in algebra are used in functional analysis, Complex analysis, operations research, computer science, Physics and Chemistry.

The aim of the course is to provide every postgraduate student a comprehensive idea about the principles of real analysis. This course will provide such treatment. This course deals with a thorough understanding of convergence, continuity and differentiation. Algebra and Analysis are the two eyes of a main in the realm of Mathematics. Analysis takes a man into the highlands of Mathematics itself, where these concepts are inseparable in all of pure mathematics as it is today. This course is the seed, which is primitive in appearance but has the capacity for vast and intricate development for an able mathematician. Real analysis is the foundation of pure Mathematics and the ideas of real analysis are used in topology, functional analysis complex analysis and measure theory.

Graph theory is an important branch of Mathematics which has plenty of applications in almost all other fields such as Physics, Chemistry, Operations Research, Management, Sociology, Linguistics, Computer engineering, Electrical engineering, etc. The objective of the course is to give a complete introduction to Graph theory and to cover very recent areas of graph theory, so that interested students can continue their research in this area. This course covers all the basic concepts in graph theory namely trees, Eulerian and Hamiltonian graphs, matching, vertex and edge coloring, planar graphs and applications of graph theory in various fields.

The aim of the course is to enable the student to sharpen his thinking capacity and logical ability and appreciate the beautiful results in number theory. This course deals with the basic topics in number theory like prime and composite numbers, congruences, quadratic residues, moebius function, arithmetic function, Diophantine equations. Number theory is a very elegant and beautiful branch of mathematics and some people call number theory as a queen of mathematics. Number theory ideas are very much used in coding theory, cryptography, communication theory, testing efficiency of algorithms and computers. It is one of the areas where Indian mathematicians made lot of contributions.

The objective of the course is to provide the students with the fundamentals of Differential Geometry in a strong and rigorous way. The students are also exposed to some relatively advanced level theorems in Differential Geometry.

C has become the starting point for learning a course on programming language. This course is mainly designed to use C to learn the art of programming, and to appreciate and understand the C language to creatively write a wide range of programmes and peep into the study of Data Structures.

 

The course will aim to provide a strong foundation in the abstract approach for the budding mathematician. In this course the students will be introduced to the third algebraic model, a vector space, field theory, algebra of linear transformation and various types of operators. One of the amazing features of twentieth century mathematics has been its recognition of the power of abstract approach. Modern algebra has evolved with this abstract approach, and is one of the important current research area of mathematics, and also serves as the unifying thread which interfaces all of mathematics – geometry, number theory, analysis, topology and even applied mathematics. These are potent and effective tools in all branches of Mathematics. These ideas trace its origin to topics in geometry and physics. The basic ideas in algebra are used in functional analysis, Complex analysis, operations research, computer science, Physics and Chemistry.

The aim of this course is to provide every postgraduate student a comprehensive idea about the principles of real analysis. This course will provide such treatment. This course will give a comprehensive treatment of integration, uniform convergence and end up with the three important results of any fundamental course in analysis namely inverse function theorem, implicit function theorem and rank theorem. Algebra and Analysis are the two eyes of a main in the realm of mathematics. Analysis takes a man into the highlands of mathematics itself, where these concepts are inseparable in all of pure mathematics as it is today. This course is the see, which is primitive in appearance but has the capacity for vast and intricate development for an able mathematician. If analysis is one of the eyes of a man in the realm of mathematics, differentiation and integration are the two eyes of a man in the realm of analysis. Real analysis is the foundation of pure mathematics and the ideas of real analysis are used in topology, functional analysis, complex analysis and measure theory.

This course will enable the students to understand the basic concepts of Differential Equations and apply them to various physical problems. This course will also initiate interest in the students in higher studies and research in applied mathematics.

The aim of this course is to help the students to understand and apply some of the widely used techniques of Operation research. The course deals with network models, dynamic and integer programming, inventory and queuing theory, nonlinear programming, and provide the mathematical basis behind these techniques. Operation research means research on operations and helps you to make optimal decisions using mathematical techniques in those situations where you have to choose the best among many different alternatives. Even though it has it’s origin during second world war for military operations now it widely used in many different field like business, industry and government. One of the many reason for growth of operation research is the simultaneous development of high speed computing without whose support real life large scale problems cannot be solved using operation techniques it is a part of the curriculum Management, Commerce, Economics, Computer science and Engineering students.

This course will enable the students to understand the basic concepts of Fluid Dynamics and apply them to various physical problems. This course will also initiate interest in the students in higher studies and research in applied mathematics.

The objective of this course is to enable the students to understand the fundamental concepts of Object - Oriented programming using C++ and to train them to apply these concepts in solving the real world problems. The course provides an understanding of the social, political, cultural and religious factors and their influence in the growth of Indian economy in the current context of globalization, liberalization and privatization.

 

The course will enable the students to master the basic concepts of topology. The course deals with the topics various topological spaces, metric spaces, compact spaces, connected spaces, countability axioms and separation axioms Topological spaces are looked upon as generalized geometric configurations and the emphasis is based on the structure of the spaces themselves. In the other direction the main stimulus has been analysis. Topology is an important area of pure mathematics in which the ideas of metric properties of real numbers are generalized. Concepts of topology are very much used in both complex analysis and functional analysis.

The aim of the course is to enable the student to understand the basic ideas of measure theory. The course deals with the concepts abstract measure spaces, abstract integration, Lebesgue measure, Lebesgue integration and the relation with Riemann integration and various types of convergence of sequence of measurable functions. Measure theory generalizes the concept of length, area, volume, summation and integration in a general setup. Modern treatment of probability theory and mathematical statistics heavily relies upon measure theory ideas. These ideas are also used in functional analysis. Both ideas from Real analysis and topology are needed to understand measure theory.

The objective of this course is to develop an ability in the students to apply statistical methods to real life problem, to understand the limitations of these methods, to think probabilistically and to generalize the statistical theory to several variables. The course deals with random variable, stochastically independence, distribution functions, conditional probability, standard theoretical distributions, sampling distributions, distributions of functions of random variable and limiting distributions Statistical tools are applied in all branches of science and humanities to verify and test various hypothesis, estimation of values of certain unknown parameters, find the relation between two or more quantities , to find meaningful inferences form raw data. In this course statistics is not dealt as statistical methods, but as the mathematical foundation of interpretation of mathematical data with rigorous mathematical treatment.

The objective of this course is to introduce to the students all the basic ideas of fuzzy mathematics. The course deals with types of fuzzy sets, operations on fuzzy sets, fuzzy number, fuzzy interval, fuzzy logic, fuzzy relations and various connectives in fuzzy sets. The ideas of pure mathematics based on set theory cannot be used in many real situations since real life phenomena like beauty, intelligence, good, rich are generally vagur and imprecise. To overcome this problem Zadeh introduced the concept of fuzzy sets in 1975. The ideas of fuzzy mathematics were widely used in management decision-making situations, medicine, engineering and logic. It is one of the areas in mathematics like graph theory where lot of research is being done and researchers rewrite all the results of pure mathematics in the new fuzzy set up.

The Objective of this course is to train the students to process data and designing a front end.

This course will enable the students to understand the basic concepts of Combinatorics and apply them to various physical problems. This course will also initiate interest in the students in higher studies and research in applicable mathematics.

This course will enable the students to understand the basic concepts of Coding theory and apply them to various physical problems. This course will also initiate interest in the students in higher studies and research in applied mathematics.

 

The aim of the course is to enable the student to understand the basic ideas of functional analysis. The course deals with normed linear spaces, Banach spaces, Hilbert spaces, bounded linear functionals, operators and projections. Students with real knowledge of real analysis and complex analysis will know that a unifying process is found to happen and this is done in this course. The abstraction process functions and the development of normed linear spaces, Banach spaces and Hilbert spaces will be studied culminating in spectral theory and operator theory. Functional analysis is an important area of pure mathematics and has wide applications in quantum mechanics, theoretical physics, control theory, approximation theory, and optimization techniques.

The aim of the course is to help the student to master all basic concepts of complex analysis. This course will provide the basic ideas of complex analysis and the students will be motivated to find interesting characteristics of real analysis and the theory of functions of complex variables and the concepts coming out of them. The course deals with the following concepts Topology of complex plane, various types of differentiation of complex functions, complex integration, relation between analytic function and power series, bilinear transformation and conformal mapping, singularities and residues and evaluation of standard integrals. Little would have Euler imagined that the introduction of the imaginary number “I” would develop a new branch of Mathematics with wide applications in Physics and related areas. Complex analysis is a fundamental branch of pure mathematics and the ideas of complex analysis are used in Physics and functional analysis. Many results that cannot be proved using real analysis can easily be proved using complex analysis.

The objective of this course is to develop an ability in the students to apply statistical methods to real life problem, to understand the limitations of these methods, to think probabilistically and to understand the estimation theory and to test hypothesis of different types. The course deals with the various types of estimators, confidence intervals for estimators, testing of statistical hypothesis, best test, distribution of quadratic form and analysis of variance. Statistical tools are applied in all branches of science and humanities to verify and test various hypothesis, estimation of values of certain unknown parameters, find the relation between two or more quantities, to find meaningful inferences from raw data. In this course statistics is not dealt as statistical methods, but as the mathematical foundation of interpretation of mathematical with rigorous mathematical treatment.

The aim of the course is to mainly study the Mathematics of the geometry of nature namely fractal geometry. The course deals basic ideas of topology required, various examples of fractals, construction of fractals, dimension of fractal and relation between code space and fractals. Fractal geometry is an emerging subject which has applications in Physics, Chemistry, Biology, Computer Science, Share market, weather forecasting etc. This course started when Mendelbrot in1982 observed the geometry of nature which has led us to think in a new scientific way about the edges of clouds, the profiles of the tops of the forest, the movement of feathers in the wings of a bird as it wells.

The objective of the course is to provide the students the techniques of programming in Java which is essential for writing programs for the internet and also to teach the methods of web designing. The topics covered in this course are Java language, applet programming, web designing and software development for internet.

To introduce the concept of parsing of a Language, and then understand the formal notion of a grammar and language. To present the hierarchy of languages formulated by Chomsky, and then its relation to Finite State Automata. To introduce the study of Context Free languages and its relation to Pushdown Automata.

This course will enable the students to understand the basic concepts of Stochastic Processes and apply them to various physical problems. This course will also initiate interest in the students in higher studies and research in applicable mathematics.

This course will enable the students to understand the basic concepts of Data Warehouse Architecture, Data Mining and its applications. The course provides an understanding of the social, political, cultural and religious factors and their influence in the growth of Indian economy in the current context of globalization, liberalization and privatization.

project is equivalent to a four credit course. A student willing to do a project has to choose a topic in consultation with a faculty member, who will be guiding and supervising the student through out the project. The outcome of the project work has to be submitted in the form of a project report for evaluation. At the end of the semester, a viva-voce will be conducted by a committee consisting of the supervisor and the two heads of the department to evaluate the project work and award credits. A total of 100 marks will be awarded as follows.