BSc (Hons) in Mathematics

This course develops learners’ English skills in reading, writing, listening, and speaking for academic and professional purposes. It covers learning approaches, grammar, sentence construction, and vocabulary enhancement. Students learn effective writing strategies, including idea generation, organization, drafting, and revision. The course also introduces modern and business communication, as well as report writing and its structure. Overall, it equips students to communicate clearly, confidently, and effectively in real-life situations.

This course provides fundamental knowledge of Mathematical Logic, Set Theory, Inequalities, Algebraic Series, Theory of Equations, and Complex Numbers. It develops logical reasoning and problem-solving skills essential for higher mathematics. Students learn inequalities, complex number properties, and applications of De Moivre’s theorem. The course also covers summation of series and methods for solving polynomial equations. Overall, it builds a strong foundation for advanced mathematical studies and applications.

This course introduces descriptive statistics to help students analyze and interpret data effectively. It covers data collection, classification, and graphical representation of populations and samples. Students learn measures of location and dispersion, along with their properties and applications. The course also includes moments, skewness, kurtosis, correlation, regression, index numbers, and time series analysis. Overall, it develops students’ skills in data interpretation and informed statistical decision-making.

This course introduces the fundamental concepts of Differential Calculus, focusing on rates of change and their applications. It covers functions, graphs, limits, continuity, and rules of differentiation, including higher-order derivatives. Students learn tangent and normal lines, partial differentiation, and applications like optimization and curve analysis. Key theorems such as Rolle’s, Mean Value, and L’ Hospital’s rule are included. Overall, it develops problem-solving skills and a strong foundation for advanced studies in mathematics and science.

This course provides fundamental knowledge of geometry by linking algebraic equations with geometric shapes. It covers coordinate systems, transformations, and equations of lines and second-degree curves. Students study detailed properties of conic sections, including circles, parabolas, ellipses, and hyperbolas. The course also includes tangents, normals, systems of circles, and key geometric parameters like focus and directrix. Overall, it develops strong geometric concepts for advanced mathematical studies and problem-solving.

This course introduces fundamental computer concepts, including hardware, basic operations, and software applications. It covers computer organization, input-output devices, processors, memory, storage, and number systems. Students learn about operating systems, data communication, networks, and the Internet. The course also teaches multimedia applications and essential skills in Microsoft Word, Excel, and PowerPoint. Overall, it equips students with both theoretical knowledge and practical skills for efficient computer use.

This course introduces the fundamental concepts of Integral Calculus, focusing on areas, volumes, and other applications of integration. It covers indefinite and definite integrals, techniques of integration, and the fundamental theorem of calculus. Students learn reduction formulas, improper integrals, and applications like curve tracing and solids of revolution. The course also includes polar coordinates, Gamma and Beta functions, and Taylor series expansions. Overall, it equips students with essential tools for advanced mathematical analysis and problem-solving.

This course introduces the fundamental concepts of Integral Calculus, focusing on areas, volumes, and other applications of integration. It covers indefinite and definite integrals, techniques of integration, and the fundamental theorem of calculus. Students learn reduction formulas, improper integrals, and applications like curve tracing and solids of revolution. The course also includes polar coordinates, Gamma and Beta functions, and Taylor series expansions. Overall, it equips students with essential tools for advanced mathematical analysis and problem-solving.

This course continues from Statistics I, introducing probability, probability distributions, sampling techniques, and hypothesis testing. It covers basic probability concepts, random variables, and expectations, as well as binomial and normal distributions. Students learn different sampling methods, including simple, stratified, and systematic sampling, and understand sampling errors. The course also introduces basic concepts of hypothesis testing to evaluate data validity. Overall, it equips students with essential tools for statistical analysis and practical data interpretation.

This course introduces the basic concepts and applications of Mathematica software for solving mathematical problems. It covers fundamental operations, strings, logical relations, loops, graphing, and user-defined functions. Students learn to generate and manipulate lists, as well as apply set theory and tables. The course also includes solving problems in Calculus, including differentiation and integration. Additionally, it covers Algebra topics such as sets, functions, equations, and matrices, using Mathematica for problem-solving.

Viva Voce on Courses taught in the 1st year.

This course introduces Real Analysis, a fundamental part of mathematics for undergraduate and higher studies. It covers real numbers as a complete ordered field, including supremum, infimum, and the denseness of rationals and irrationals. Students learn the topology of the real line, including open and closed sets, limit points, compactness, and connected sets. The course also covers real sequences, convergence, Cauchy sequences, and infinite series with convergence tests. Overall, it develops rigorous mathematical reasoning and analytical skills.

This course covers advanced topics in Differential and Integral Calculus, focusing on rates of change and area or volume calculations. It includes vector-valued functions, their limits, derivatives, integrals, tangent lines, and arc length. Students learn functions of several variables, partial derivatives, extrema, saddle points, Lagrange multipliers, and Taylor’s formula. The course also introduces multiple integration, including double and triple integrals in various coordinate systems. Overall, it develops strong analytical and problem-solving skills in multivariable calculus.

This course introduces differential equations and their importance in modeling real-world phenomena in engineering, physics, economics, and other fields. It covers ordinary differential equations, their classification, solutions, and initial and boundary value problems. Students learn methods for solving first-order equations and applying them to practical models like growth, decay, heating, cooling, and circuits. The course also covers higher-order linear differential equations, including solution methods and fundamental theory. Overall, it equips students with skills to model and solve real-world problems using differential equations.

This course introduces numerical analysis, focusing on algorithms for approximating solutions to mathematical problems. It covers solving equations in one variable using methods like bisection, false position, and Newton-Raphson, with error analysis. Students learn interpolation and polynomial approximation, including Taylor and Lagrange methods. The course also covers numerical differentiation and integration using various rules and techniques. Additionally, it teaches solving linear systems, matrix operations, and LU decomposition for practical applications in science and engineering.

This course introduces Linear Algebra, a fundamental component of mathematics essential for undergraduate studies. It covers vectors in 2D and 3D space, inner products, norms, and distances. Students learn about matrices, determinants, their properties, and operations, including inverses and Cramer’s rule. The course also covers systems of linear equations, both homogeneous and non-homogeneous, and methods to solve them using matrices and determinants. Overall, it equips students with essential tools for mathematical problem-solving and applications.

This course introduces fundamental concepts of computer science and essential computer skills. It covers computer hardware and software, operating systems, types of memory, and number systems. Students learn digital logic, including logic gates, Boolean algebra, and basic components like counters and adders. The course also introduces basic programming in C, computer networks, and network concepts. Additionally, it covers Internet protocols, applications, and basic computer security, including viruses and spyware.

This course provides an in-depth study of Linear Algebra, a fundamental component of mathematics. It covers vector spaces, subspaces, linear combinations, independence, span, basis, and dimension, as well as row, column, and null spaces of matrices. Students learn about linear transformations, including kernel, image, rank, nullity, and matrix representations. The course also introduces eigenvalues and eigenvectors, diagonalization, matrix polynomials, and the Cayley-Hamilton theorem. Overall, it equips students with essential tools for advanced mathematical analysis and applications

This course introduces numerical analysis, focusing on algorithms for solving scientific and engineering problems. It covers iterative techniques in matrix algebra, including solving linear systems and finding eigenvalues. Students learn numerical solutions for nonlinear systems using fixed-point, Newton’s, and quasi-Newton methods. The course addresses initial value problems for ODEs with Euler, Runge-Kutta, and multi-step methods, including error analysis. It also covers boundary value problems and implementing numerical methods in FORTRAN.

This course introduces Complex Analysis, focusing on functions of a complex variable and their applications in mathematics, engineering, and physics. It covers complex numbers, analytic functions, and Cauchy-Riemann equations. Students learn complex integration, including Cauchy’s theorems and the residue theorem. The course also addresses power series, Taylor and Laurent expansions, and singularities. Additionally, it introduces conformal mappings, meromorphic functions, and applications in solving differential equations.

This course introduces students to solving problems using two-dimensional and three-dimensional graphics, as well as Differential and Integral Calculus. It covers 2D graphics, including plotting single-variable functions, special plots, and animation. Students learn 3D graphics, plotting functions of two variables, and 3D primitives. The course also includes Differential Calculus topics like limits, derivatives, and maxima and minima. Additionally, it covers Integral Calculus, including anti-derivatives, definite integrals, and functions defined by integrals.

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This course introduces Real Analysis, focusing on limits, continuity, and differentiability of real functions. It covers integration using Riemann sums, the fundamental theorem of calculus, and related properties. Students learn sequences and series of functions, including uniform convergence and key convergence tests. The course also addresses Euclidean n-spaces, norms, distance, convergence, and compactness. Overall, it develops a strong foundation in rigorous mathematical analysis and multi-variable calculus.

This course introduces Abstract Algebra, emphasizing its importance in mathematics and other sciences. It covers relations, including equivalence relations, congruence, and binary relations. Students learn about groups and subgroups, including permutation, cyclic, symmetric, and alternating groups. The course addresses cosets, Lagrange’s theorem, and homomorphisms, isomorphisms, and quotient groups. It also explores practical applications of group theory in various fields.

This course covers advanced differential equations and their applications in science and engineering. It introduces existence and uniqueness theorems for single equations, systems, and higher-order equations. Students learn series solutions of second-order linear equations, including Frobenius method and special functions. The course addresses systems of linear first-order differential equations using matrix methods and variation of parameters. It also covers eigenvalue problems, Sturm–Liouville boundary value problems, and Green’s functions.

This course introduces Vector Calculus, focusing on differentiation and integration of vectors. It covers scalar and vector fields, directional derivatives, and tangent planes. Students learn gradient, divergence, curl, and their properties. The course includes line, surface, and volume integrals of vector functions. It also covers key theorems, including Green’s, Gauss’s divergence, and Stokes’ theorems, with applications.

This course introduces the fundamental concepts of mechanics, covering both statics and dynamics. It includes the study of forces, equilibrium of particles in plane and space, and resolution of concurrent forces. Students learn about the center of gravity for curves, areas, surfaces, and volumes. The course also covers the equilibrium of flexible strings and chains, including catenary equations. Additionally, it introduces rectilinear motion and simple harmonic motion with Hooke’s law and geometric representations.

This course introduces Linear Programming, a method for optimizing outcomes in problems with linear relationships. It covers convex sets, feasible and optimal solutions, and basic theorems of feasibility and optimality. Students learn to formulate linear programming problems and solve them using graphical and simplex methods. The course also addresses duality, including primal and dual problems, and related theorems. Additionally, it covers sensitivity analysis and practical applications of linear programming.

This course covers Abstract Algebra-II, focusing on rings, integral domains, and fields. It introduces various types of rings, their properties, subrings, ideals, and prime and maximal ideals. Students learn about integral domains, division rings, quotient rings, and ring homomorphisms and isomorphisms. The course also covers principal ideal domains, Euclidean domains, unique factorization domains, and polynomial rings with applications like Gauss’s theorem and irreducibility criteria. Additionally, it introduces fields, their types, and the structure of prime fields.

This course covers Methods of Applied Mathematics, focusing on Fourier and Laplace transforms for solving differential equations. It includes Fourier series, their properties, and applications, as well as special functions like Gamma, Error, and Hypergeometric functions. Students learn Laplace transforms, inverse transforms, and their use in solving ODEs and boundary value problems. The course also introduces Fourier transforms, including sine and cosine transforms and the convolution theorem. Overall, it develops tools for solving applied mathematical and physical problems.

This course introduces differential equations and methods to solve various mathematical problems. It covers first-order equations, including general and complete solutions, Cauchy problems, and methods like Lagrange’s and Charpit’s. Students learn second-order equations, classification, canonical forms, and characteristic curves. The course addresses boundary value problems, Fourier methods, and applications in cylindrical and spherical coordinates. Additionally, it includes transform methods, such as Laplace and Fourier sine and cosine transforms, for solving inhomogeneous equations.

This course introduces Tensor Analysis, an advanced mathematical tool for studying dynamic and conceptual physical problems. It covers vectors and tensors in curvilinear coordinates, including contravariant and covariant vectors and coordinate transformations. Students learn Riemannian metrics, metric tensors, and Christoffel symbols, with applications in three-dimensional Euclidean space. The course addresses covariant differentiation of tensors and curvature tensors. Additionally, it covers curvature of curves, geodesics, and Riemannian coordinates for analyzing physical and geometric problems.

This course develops numerical methods using technology to solve problems in algebra, calculus, geometry, and differential equations. Students learn to solve linear systems, evaluate limits, continuity, maxima, and minima of functions. The course covers numerical solutions of definite integrals and algebraic or transcendental equations. It also addresses matrix operations, eigenvalues, eigenvectors, canonical forms, and applications like linear programming and Markov chains. Additionally, students learn to solve first- and higher-order differential equations, including series solutions.

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This course introduces Topology, focusing on properties of spaces that remain invariant under continuous transformations. It covers metric spaces, including open and closed sets, convergence, completeness, and continuous mappings. Students learn topological spaces, bases, sub-bases, and weak topologies, along with function algebras. The course addresses compactness, Tychonoff’s theorem, and locally compact spaces. Additionally, it covers separation axioms and connectedness, including locally connected and path wise connected spaces.

This course introduces Number Theory, focusing on the properties of integers and natural numbers. It covers congruences, including Fermat’s, Euler’s, Wilson’s, and Lagrange’s theorems, and the Chinese remainder theorem. Students learn arithmetical functions, Dirichlet convolution, and arithmetic in quadratic fields. The course addresses quadratic residues, Diophantine equations, and sums of squares. Additionally, it covers continued fractions, surds, and the arithmetic of simple and complex quadratic fields.

This course introduces special functions and their applications in solving mathematical problems. It covers Legendre functions, including differential equations, recurrence relations, and associated functions. Students learn Bessel functions, their properties, integral representations, and orthogonality. The course addresses Laguerre polynomials with generating functions, Rodrigues’ formula, and recurrence relations. It also includes Hermite polynomials, their differential equations, orthogonal properties, and expansion theorems.

This course covers mechanics, including statics and dynamics, and methods to solve related problems. It addresses motion in a plane and in space, with velocity, acceleration, and central forces. Students learn the motion of rigid bodies, kinetic energy, and angular momentum. The course covers moment of inertia, including products of inertia and momental ellipsoids. It also includes D’Alembert’s principle and motion about fixed axes, such as pendulums

This course introduces fluid mechanics, covering fundamental equations and their applications in engineering problems. It addresses kinematics of fluid particles, including velocity, acceleration, and flow patterns. Students learn equations of motion, such as Euler’s, Bernoulli’s, and vorticity equations. The course covers two-dimensional motion, circulation, vorticity, and theorems like Kelvin’s and Blasius. It also includes sources, sinks, doublets, complex potentials, and applications to flow around cylinders.

This course introduces Functional Analysis and its applications in solving partial differential equations and other mathematical problems. It covers inner product spaces, orthogonality, and orthonormal sets. Students learn function spaces, Banach spaces, continuous linear transformations, and key theorems like Hahn-Banach and Open Mapping. The course also addresses Hilbert spaces, orthogonal complements, and operator conjugates. Additionally, it includes fixed point theory, Banach contraction and Schauder principles, and applications to existence and uniqueness of solutions.

This course introduces Differential Geometry, linking vector geometry, calculus, and algebra. It covers space curves, including tangents, normals, osculating planes, curvature, torsion, helices, involutes, and evolutes. Students study surfaces using curvilinear coordinates, first and second fundamental forms, and metric properties. The course includes principal curvatures, Gaussian and mean curvature, lines of curvature, and centers of curvature. Applications of Euler’s theorem, Dupin indicatrix, and classification of points on surfaces are also discussed.

This course, Honors Project, is a research-based project offered in the final year, second semester. It allows students to conduct independent research and produce a substantial thesis. The project integrates knowledge gained throughout the undergraduate program. Students develop analytical, judgmental, and communication skills through their research work. Evaluation includes a viva-voce and defense based on Year-4 coursework and the project report.

This course teaches programming in Mathematica for solving advanced mathematical problems. It covers multivariate calculus, including partial derivatives, maxima and minima, total differentials, and multiple integrals. Students learn analytical and numerical solutions of ordinary differential equations, including Laplace transforms. Linear algebra topics include vectors, matrices, matrix operations, eigenvalues, eigenvectors, and canonical forms. Overall, it develops practical skills to apply mathematics using computational tools.

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