Undergraduate Program

Course Credit: 3

Fundamentals of Mathematics are the foundations of all mathematics courses the course is very productive. Understanding of this course will precede everyone to learn other areas of mathematics. After completion of this course, students will get some useful and applicable ideas on mathematical logic, methods of proofs, set theory, real and complex number system, inequality, relations and functions with graphs, equations, various types of series, and vectors.

Course Credit: 2

This course deals with the study of rates of change and provides a framework for modeling systems in which there is change and way to deduce the predictions of such models. Here we study two types of calculus: Differential calculus and integral calculus for single variable functions. Differential calculus controls the rate of change of a quantity whereas integral calculus discoveries the quantity where the rate of change is known. The course Calculus-I covers topics of differential and integral calculus including limits and continuity, higher-order derivatives, curve sketching, differentials, indefinite and definite integrals (areas, arc lengths and volumes) and applications of derivatives and integrals

Course Credit: 3

Calculus is one of the most fundamental courses in Mathematics which majorly contains two parts (Differential and Integral). The course Differential calculus I mainly contains the initial part of Differential calculus (Single variable function). Understanding this course will lead everyone to learn the other mathematical courses which needs the fundamentals of differentiation. After completing this course students will learn the basic idea of function, limits and continuity of functions, graphical representation of different functions, analysis of functions, basics of differentiation and the applications involving differentiation in different sectors of real life.

Course Credit: 2

Analytic Geometry is a branch of algebra that is used to represent geometric objects - points, straight lines, planes and conics being the most basic of these. Our goal is to develop skills on 2- dimensional and 3-dimensional geometry which includes theory and some real life applications problems on coordinate systems, conic sections, pair of straight lines, planes and lines, conicoids. After finishing this course, students will able to explain the physical meaning of graphs, geometrical formula and equations. Also students will relate the theory with the real world phenomena.

Course Credit: 3

Analytic Geometry is a branch of algebra that is used to model geometric objects - points, (straight) lines, and circles being the most basic of these. Analytic geometry is a great invention of Descartes and Fermat. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space (three dimensions). The importance of analytic geometry is that it establishes a correspondence between geometric curves and algebraic equations. This correspondence makes it possible to reformulate problems in geometry as equivalent problems in algebra, and vice versa; the methods of either subject can then be used to solve problems in the other. For example, computers create animations for display in games and films by manipulating algebraic equations.

Course Credit: 3

Linear algebra is an essential part of the curriculum of majors such as: Computer science, Engineering, Economics, Physics, and Mathematics. It has a broad range of applications in those areas. For most students, Linear Algebra is the first course that blends computational and conceptual aspects of mathematics.The study of linear algebra is motivated by the geometry of problems in two and three dimensions. A clear understanding of the concepts of linear algebra is essential for the proper description and representation of all physical and mathematical phenomena in higher dimensions. The algorithms of linear algebra are also central to the theory of scientific computing and numerical analysis. A first course in linear algebra serves as an introduction to the development of logical structure, deductive reasoning and mathematics as a language. For students, the tools developed from a course in linear algebra will be as fundamental in their professional work as the basic tools of calculus. For these reasons, this course is a core course for students pursuing a major in mathematics.

Course Credit: 2

Linear algebra is an essential part of the curriculum of majors such as: Computer science, Engineering, Economics, Physics, Chemistry and Mathematics. It has a broad range of applications in those areas. For most students, Linear Algebra is the first course that blends computational and conceptual aspects of mathematics. In an increasingly complex world, mathematical thinking, understanding, and skill are more important than ever. This course will show students how to simplify many types of complex problems using matrix algebra and vector geometry. Students who major in the sciences or engineering are often required to study linear algebra. This course provides a solid foundation for further study in mathematics, the sciences, and engineering.

Course Credit: 3

In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with differentiation, integration is a fundamental operation of calculus,and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others.

Course Credit: 3

Elementary Number Theory is the study of the basic structure and properties of natural numbers. Learning Number Theory helps improving one's ability of mathematical thinking. After completion of this course, students will prove results involving divisibility and greatest common divisors; solve systems of linear congruence’s; find integral solutions to specified linear Diophantine Equations; apply Euler-Fermat’s Theorem to prove relations involving prime numbers; apply the Wilson’s

Course Credit: 3

Problems in the courses of First Year BSHonours will be solved using Computer Algebra System (CAS) MATHEMATICA.

Course Credit: 2

Viva Voce on courses taught in the First Year.

Course Credit: 3

As the functions of real variable models natural events, it is important to understand the properties of a function of a real variable. This course gives a proper treatment in understanding of the real number set which facilitates the subsequent properties of a function beyond the informal treatment of objects in calculus.

Course Credit: 2

Multi-variable calculus is the extension of calculus to more than one variable. Single variable calculus is a highly geometric subject and multivariable calculus is the same, maybe even more so. In calculus class, student’s studied the graphs of functions z =f(x, y) and w = f(x, y, z) and learned to relate derivatives and integrals to these graphs. One key difference is that more variables mean more geometric dimensions. This makes visualization of graphs both harder and more rewarding and useful

Course Credit: 3

Calculus, the branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus). Calculus is considered to be one of the greatest achievements of the human intellect and it is now the basic entry point for anyone wishing to study physics, chemistry, biology, economics, finance, or actuarial science. The development of calculus in the seventeenth and eighteenth centuries was motivated by the need to understand physical phenomena such as the tides, the phases of the moon, the nature of light, gravity etc.

Course Credit: 2

The construction of mathematical models to address real life problems has been one of the most important aspects of each of the branches of science. These mathematical models are formulated in terms of equations involving functions and their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. Ordinary differential equations (ODEs) are a fundamental part of the mathematical vocabulary used to describe natural phenomena. The course emphasizes classical methods for finding exact solution formulas. After completion of this course, the students will get some useful and applicable ideas for modeling physical and other phenomena.

Course Credit: 3

The construction of mathematical models to address real life problems has been one of the most important aspects of each of the branches of science. These mathematical models are formulated in terms of equations involving functions and their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. Ordinary differential equations (ODEs) are a fundamental part of the mathematical vocabulary used to describe natural phenomena. The course emphasizes classical methods for finding exact solution formulas. After completion of this course, the students will get some useful and applicable ideas for modeling physical and other phenomena.

Course Credit: 2

Numerical analysis, area of mathematics and computer science that creates, analyzes, and implements algorithmsfor obtaining numerical solutions to problems involving continuous variables. Such problems arise throughout the natural sciences, social sciences, engineering, medicine, and business. Numerical analysis is concerned with all aspects of the numerical solution of a problem, from the theoretical development and understanding of numerical methods to their practical implementation as reliable and efficient computer programs. Most numerical analysts specialize in small subfields, but they share some common concerns, perspectives, and mathematical methods of analysis

Course Credit: 3

Linear algebra II is the study of vector spaces and linear mappings between them. In this course, we will begin by reviewing topics you learned in Linear Algebra I, starting with vectors, matrices and linear mappings. The review will refresh the student's knowledge of the fundamentals of vectors and of matrix theory, and how to perform operations on matrices. After the review, we can extend this idea to Similar Matrices. Next, we will focus on Linear Functional and dual Space. We will then introduce a new structure on vector spaces: an inner product. Inner products allow us to introduce geometric aspects, such as length of a vector, and to define the notion of orthogonality between vectors. In this context, we will study the applications in Linear Models and Fourier Approximation, and more. We will end this chapter with the spectral theorem, which provides a decomposition of the vector space on which operators act, and singular-value decomposition, which is a generalization of the spectral theorem to arbitrary matrices. Then, we will study Bilinear, quadratic & hermitian forms. Symmetric Matrices and Quadratic Forms, Positive Definite Matrices will be studied at the end of this course with their applications in diverse fields. The subject material is of vital importance in all fields of mathematics and in science in general.

Course Credit: 3

Calculus is a branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus). Calculus is considered to be one of the greatest achievements of the human intellect and it is now the basic entry point for anyone wishing to study physics, chemistry, biology, economics, finance, or actuarial science. The development of calculus in the seventeenth and eighteenth centuries was motivated by the need to understand physical phenomena such as the tides, the phases of the moon, the nature of light, gravity etc.

Course Credit: 3

Numerical Method is an important branch in Mathematics as well as Engineering. It aims at numerically solving all kinds of mathematical problems which arise from practical applications and can be modeled by different mathematical equations.

Course Credit: 2

Linear algebra is a branch of mathematics that studies systems of linear equations and their representations in vector spaces and through matrices. The concepts of linear algebra are extremely useful in physics, economics and social sciences, natural sciences, and engineering. Due to its broad range of applications, linear algebra is one of the most widely taught subjects in university level mathematics

Course Credit: 3

Discrete mathematics deals with fundamental ideas of reasoning, counting, recurrence relations and graph theory. Understanding of this course will help students to learn the bridging of mathematics with computer science. After completion of this course, students will get some useful and applicable ideas on mathematical logic, recurrence relations, generating functions, different graphs. It will enable them to use algorithms on graphs to solve some well-known problems.

Course Credit: 3

Programming Fundamentals is the basic foundation course for mathematical programming. Students will learn the basics of program design techniques. After completion of this course they will be able to solve mathematical and scientific problems through computer program. Though programming language covered here is Fortran but students will be able to learn other languages for mathematical programming very quickly after completion of this course.

Course Credit: 3

Problems in the courses of Second Year BS Honours will be solved using Computer Algebra System (CAS) MATLAB.

Course Credit: 2

Viva Voce on courses taught in the Second Year.

Course Credit: 3

This course will focus on advance topics in ordinary differential equations. It will analyze existence and uniqueness theorem of ODE. It will also study on series solutions of second ordered linear ordinary equations. This course will also focus on Legendre functions, Bessel’s function and Hermite polynomials.

Course Credit: 3

Abstract algebra is the set of advanced topics of Algebra that deal with abstract algebraic structures rather than the usual number systems. It aims to find general underlying principles common to the usual operations (addition, multiplication, etc.) on diverse sets such as integers, polynomials, matrices, permutations, and much more. Students will learn in particular about the most important abstract algebraic structures which are groups, rings, and fields. It gives to student a good mathematical maturity and enables to build mathematical thinking and skill. Important branches of abstract algebra are commutative algebra, representation theory, and homological algebra.

Course Credit: 3

This course is about the study of elementary properties of topological spaces. Topological spaces turn up naturally in mathematical analysis, abstract algebra and geometry. A topological space is a structure that allows one to generalize concepts such as convergence, connectedness and continuity.

Course Credit: 3

This course focus on the approximation methods for solving matrix algebra, system of linear equations and system of nonlinear equations. This course also introduces different approximation methods for ordinary differential equations (ODEs), initial value problems (IVPs), boundary value problems (BVPs). It also focus on finite difference method for partial differential equations (PDEs).

Course Credit: 3

This is an advanced mathematics course which is proposed to give an overview of mathematical methods widely used in physical sciences. Fourier series, Laplace transforms, Fourier transforms, Eigenvalue problems and Strum-Liouvile boundary value problems will be studied. Here we focus on the application to solve real life problems. After taking this course, students will become familiar with new mathematical skills.

Course Credit: 3

Optimization is one of the greatest successes to emerge from operations research and management science. It is an art of finding minima or maxima of some objective function, and to some extend an art of defining the objective functions. This course will focus on the optimization techniques such as linear programming (LP), nonlinear programming (NLP) and quadratic programming (QP). This is an interdisciplinary branch of applied mathematics and formal science that uses methods like mathematical modeling, statistics, and algorithms to arrive at optimal or near optimalsolutions to real life problems and closely relates to IndustrialEngineering. It is a tool for solving optimization problems. In 1947, George Dantzig developed an efficient method, the simplex algorithm, for solving linear programming problems. Since the development of the simplex algorithm, LP, NLP and QP have been used to solve optimizationproblems in industries as diverse as banking, education, forestry, petroleum, and trucking.

Course Credit: 3

First course in stochastic area; moving from distribution to stochastic process. Brownian motion and its properties have been discussed and how these properties characterize a stochastic process in Black and Scholes world have been considered. Crucial for students developing into Mathematical Finance, Actuarial Science and stochastic area of Mathematical Biology for further studies. Fundamental differences between classical calculus and stochastic calculus have been explored through Ito's formula. Firsthand stochastic differential equations have been studied with stock price modelling in view; filtration and sigma-algebra structures, and information flow in stochastic world, are introduced. Foundational course for research development in stochastic environment.

Course Credit: 3

Actuaries are the back bone for the insurance company. Without them, there is no concept of insurance company. They work for insurance companies and predict the profitability of various customers by using the mathematical and statistical formulas. Actuaries estimate the present value cost for future uncertainty like accidents, deaths, natural disaster, disability and lawsuits. Actuaries are engaged in life insurance, retirement benefit consultancies, asset management, postretirement medical benefit, the cost of retirement benefit plans. They also involved in periodic valuation of life insurance business, pensions and other investment benefits liabilities.

Course Credit: 3

Problems in the courses of Third Year BS Honours will be solved using Programming LanguageFORTRAN.

Course Credit: 2

Viva Voce on courses taught in the Third Year.

Course Credit: 3

This course is a continuation of elementary analysis of functions of single real variable to the elementary analysis of functions of several variables. To facilitate the analysis, required topological ideas of metric spaces. Their elementary properties and the basics of functions defined on a metric space are the objects of studies at the beginning of the course. The course provides the main background needed in modern Advanced Mathematics related to Real Analysis.

Course Credit: 3

Complex analysis, which is mainly the theory of complex functions of a complex variable. The course is introduced to the basic idea of the complex plane, along with the algebra and geometry of complex numbers, and then move on to differentiation, integration, complex dynamics, power series representation and Laurent series. Majorly this course contains the integration of a complex function and theorems related to complex integration. Also the course contains the general representation of complex numbers and functions with the special idea of different complex mappings too. After completing the course, students will gain the basic ideas of complex numbers, complex functions and theorems related to complex differentiation, integration and applications of these theorems to solve different mathematical problems.

Course Credit: 3

This course will cover the foundations of functional analysis in the context of topological linear spaces and normed linear spaces. It will start with a review of the theory of general linear spaces. The linear analysis on Hilbert spaces with its rich geometrical structures will be studied with normed linear spaces. Uniform Boundedness Principle, Open Mapping Theorem and Closed Graph Theorem will be presented and several applications will be analyzed. The important notion of duality will be developed in Banach and Hilbert spaces. Bounded and unbounded self-adjoint operators in Hilbert spaces will be analyzed. Further, Banach Fixed point theorem with applications, Schauder fixed point theorem, Frechet derivative and Newton’s method for nonlinear operators will be introduced.

Course Credit: 3

This course is an introduction to measure and integration theory, and their applications to the approximation of real valued functions. The course focuses on the generalization of idea of length, area, and volume of a subset of Euclidean space to the so-called measure of a set. The idea of measure broadens the class of integrable functions compared to the Riemann integrable functions. Then we study convergence for sequences of integrable functions. The course is designed to provide the elementary introduction needed for an advanced abstract course on Measure and Integration.

Course Credit: 3

Partial differential equations (PDE) is an important branch of Science. It has many applications in various physical and engineering problems. The idea of the course is to give a solid introduction to PDE for advanced undergraduate students. We require only advanced calculus. The course goes quite rapidly through a lot of material, but our focus is linear second order uniformly elliptic, parabolic and hyperbolic equations. In this course mainly we attempt to give some ideas about first order and second order linear PDEs. A few Nonlinear PDE is discussed shortly. The method of solving first-order and second order equations are illustrated taking many examples.

Course Credit: 3

Differential geometry is based on three dimensional basic vectors geometry with calculus. Tensor calculus forms an essential part of the mathematical background required to applied mathematicians, physicists, space scientists and engineers. It’s widely used in many branches of pure and applied mathematics. Indeed the algebraic properties of tensors form the subject matter of linear algebra, while their differential properties that of differential geometry. Understanding of this Course will precede students to learn other areas of mathematics such as Geometry of Differential Manifolds, General Theory of Relativity, Cosmology, Riemannian Geometry etc.

Course Credit: 3

Mechanics describes the behavior of a body, in either a beginning state of rest or of motion, subjected to the action of forces. Applied mechanics, bridges the gap between physical theory and its application to technology. It is used in many fields of engineering, especially mechanical engineering and civil engineering. In this context, it is commonly referred to as Engineering Mechanics. Much of modern engineering mechanics is based on Isaac Newton's laws of motion while the modern practice of their application can be traced back to Stephen Timoshenko, who is said to be the father of modern engineering mechanics.

Course Credit: 3

The course deals with theoretical and practical aspects of hydrodynamics and fluid dynamics. The various topics covered are: Reynolds Transport Theorem, conservation of mass, momentum and energy, the development of the Navier-Stokes' equation, ideal and potential flows, vorticity, hydrodynamic forces in potential flow. Some of the vital topics covered are boundary layer concept, governing equations, incompressible flows, compressible flows, high speed flows, internal flow, external flow, dimensional analysis, and introduction to computational fluid dynamics.

Course Credit: 3

Combinatorics is a field of mathematics concerned with counting and finite structures. It is the study of discrete structures, which are ubiquitous in our everyday lives. While combinatorics has important practical applications (for example to networking, optimization, statistical physics, etc.), problems of a combinatorial nature also arise in many areas of pure mathematics such as algebra, probability, topology and geometry. The goal of this course is to introduce a variety of techniques and ideas that will help to solve a wide range of problems.

Course Credit: 3

Fuzzy Mathematics is based on fuzzy set theory. Fuzzy set theory is the study on fuzzy logic which is based on fuzzy sets, introduced by L. A. Zadeh in 1965, and symbolic logic. Fuzzy set theory is generalization of abstract set theory. Because of the generalization, it has a much wider scope of applicability than abstract set theory in solving various kinds of real physical world problems, particularly in the fields of pattern classification, information processing, control, system identification, artificial intelligence, and, more generally, decision processes involving uncertainty, impreciseness, vagueness, and doubtful data.The notation, terminology, and concept of Fuzzy Mathematics are helpful for students to obtain primary idea in studying and solving various kinds of real physical world problems.

Course Credit: 3

Mathematics is playing an important role in the physical and biological sciences. It has genuine uses in biology (as well as physical sciences) describing some models in population biology and the mathematics that is useful in analyzing them. Knowledge of dynamical properties is crucial in determining the existence and stability of associated solutions (equilibria) of the models. The goal of this course is to use mathematics as a tool for gaining a deeper understanding of biological systems and their dynamics.

Course Credit: 3

Scientific computing and simulations play a vital role in various areas of science ranging from biology to modeling of complex physical systems. Various algorithms and mathematical methods are used in computing and simulations. Scientific computing is now considered as another distinct mode of science and it complements and builds relation between theory and experimentations. This course will help to formulate a model of a practical phenomenon, then to develop an algorithm after discretizing the model and finally, the execution of the algorithm as a computer programming.

Course Credit: 3

Continuation of 3rd year module ‘Stochastic Calculus’ to the modern Mathematical Finance area. The domain of stochastic processes, mainly Brownian motion, in the application area of mathematical finance has been introduced with rigorous structural studies. Celebrated Black and Scholes model has been introduced, derived and intuitively explained which paves the path to study more advanced jump processes and ARCH/GARCH processes in mathematical finance area in MS.

Course Credit: 3

The aim of stochastic programming (SP) is precisely to find an optimal decision in problems involving uncertain data. In this terminology, stochastic is opposed to deterministic and means that some data are random, whereas programming refers to the fact that various parts of the problem can be modeled as linear or nonlinear mathematical programs. The field, also known as optimization under uncertainty, is developing rapidly with contributions from many disciplines such as operations research, economics, mathematics, probability, and statistics.

Course Credit: 3

Any mathematical topic not covered in other courses may be offered under this title. The course-teacher will prepare an outline of the course and obtain the approval of the departmental academic committee.

Course Credit: 3

Problem Solving in concurrent courses using any programming language: MATHEMATICA/MATLAB/FORTRAN/C/Mapple.

Course Credit: 3

Each student is required to work on a project and present a project report for evaluation. Such projects should be extensions or applications of materials included in different honours courses and may involve field work and use of technology. There may be group projects as well as individual projects.

Course Credit: 2

Viva Voce on all the courses taught at Fourth Year.