DEPARTMENT OF MATHEMATICS
B. Sc. Mathematics
After the successful completion of this course, the student will: ·
On completion of this course, successful students will be able to:
CO1- Understand the fundamental concepts and principles of mathematical logic, sets and set operations, relations, theory of equations.
CO2 - Demonstrate proficiency in operations on propositions, set operations, relations and identify polynomial equations.
CO3 - Analyse rules and theorems on logic, sets, relations and polynomial equations.
CO4 - Applications and problems based on the logic, sets, relations and polynomial equations
On completion of this course, successful students will be able to:
CO1 - Understand the properties and characteristics of conic sections including their tangents and normal lines and parametric equations , poles and polar, conjugate diameters
CO2 - Apply polar coordinates to represent and analyse geometric shapes, including lines circles and conic sections, Determine polar equations of tangents, normal and chords of conic sections
CO3 - Demonstrate proficiency in trigonometric functions of complex variable including separating them into real and imaginary part, factorization and summation of infinite series
CO3 - Develop a solid understanding of differential calculus concepts including successive differentiation and analysis of indeterminate forms
CO1 –Apply the concepts of Differential Calculus including Maclaurins Theorem, Tailors Theorem, Concavity, Points of inflections, Curvature, evolutes, and asymptotes to analyse and characterize functions
CO2: Utilize the principles of partial differentiation, including the chain rule and Lagrange multipliers, to solve problems involving functions of multiple variables, extreme values, and saddle points.
CO3: Apply integral calculus techniques, such as finding volumes using cross-sections and cylindrical shells, calculating arc lengths, and determining areas of surfaces of revolution, to solve relevant problems in mathematics and real-world applications.
CO4: Demonstrate proficiency in multiple integrals, including double and triple integrals over different coordinate systems, computing areas by double integration, and applying substitutions in multiple integrals.
After completing this course the learner should be able to
CO1: Apply vector differentiation techniques, including vector equations, parametric equations for lines and planes, vector functions, arc length, unit tangent and normal vectors, curvature, and directional derivatives, to solve problems in vector calculus.
CO2: Understand and apply vector integration concepts, such as line integrals, work, circulation, flux, path independence, conservative fields, potential functions, surface integrals, and the theorems of Green, Stokes, and Divergence, to analyse vector fields and solve relevant problems.
CO3: Demonstrate a comprehensive understanding of number theory principles, including congruence, Fermat's theorem, Wilson's theorem, and Euler's phi function, and apply them to solve problems related to number theory.
CO4: Apply Laplace transform techniques, including linearity, shifting theorem, transforms of derivatives, solution of ordinary differential equations, convolution, and integral equations, to solve differential equations and initial value problems.
FIFTH SEMESTER
After completing this course the learner should be able to
CO1: Develop a comprehensive understanding of the real numbers, including their algebraic and order properties, absolute value, completeness property, and applications of the supremum property in solving problems related to intervals and sets.
CO2: Analyse sequences and their limits, demonstrate proficiency in using limit theorems, and apply these concepts to study monotone sequences, subsequence’s, and properly divergent sequences.
CO3: Evaluate and determine the convergence of series, including absolute convergence, and apply tests for both absolute and non-absolute convergence to various mathematical series.
CO4: Gain proficiency in understanding and applying the concept of limits of functions, utilizing limit theorems, and exploring extensions of the limit concept in various scenarios.
After studying this course the students should be able to
CO1: Understand the fundamental concepts of differential equations, including the nature of solutions, separable equations, first-order linear equations, exact equations, and orthogonal trajectories, and apply these concepts to solve relevant problems.
CO2: Analyse second-order linear differential equations with constant coefficients, apply methods like the method of undetermined coefficients and variation of parameters to solve higher-order linear equations, and use known solutions to find other solutions.
CO3: Demonstrate proficiency in power series solutions and special functions, including series solutions of first-order and second-order linear equations, ordinary points, and regular singular points, with a special focus on Legendre's equations.
CO4: Develop a strong understanding of partial differential equations, including the methods of solution for linear first-order partial differential equations and Lagrange's method, and analyse integral surfaces passing through given curves.
After completing this course the learner should be able to
CO1: Demonstrate a solid understanding of abstract algebra, including groups and subgroups, binary operations, isomorphism’s, finite groups, cyclic subgroups, and elementary properties of groups.
CO2: Analyse permutations, cosets, and direct products in abstract algebra, and apply concepts like Cayley's theorem, orbits, cycles, and the theorem of Lagrange to solve problems related to groups of permutations.
CO3: Apply homomorphisms and factor groups concepts, including properties of homomorphisms, the Fundamental Homomorphism theorem, normal subgroups, inner automorphisms, and simple groups, to study and solve problems related to abstract algebra.
CO4: Gain proficiency in understanding rings and fields, including definitions, basic properties, homomorphisms, isomorphisms, integral domains, divisors of zero, cancellation, and factor rings, and apply these concepts to solve problems in abstract algebra.
After the completion of this course the student will be able to:
CO1 Explain ecosystem and various kinds of natural resources(Understand)
CO2 Determine various environmental issues and associated problems(Apply)
CO3 Analyze the role of Fibonacci numbers in Earth, flowers, sunflowers, pinecones
bees, subsets, sewage treatment, atoms, reflections, music, and compositions.(Analyze)
CO4 Apply Golden ratio in various real life situations(Apply)
Open course
After the completion of this course the student will be able to
CO1 Understanding the basic operations of Mathematics
CO2 Apply mathematical concepts and principles to solve real life problems
CO3 Solve basic problems on differentiation and integration
CO4 Identify the definitions of trigonometric ratios and their applications to
problems involving heights and distance
SIXTH SEMESTER
After the completion of this course the student will be able to:
CO1: Demonstrate a comprehensive understanding of continuous functions, including combinations of continuous functions, continuous functions on intervals, uniform continuity, and the properties of monotone and inverse functions.
CO2: Analyze differentiation concepts, including the derivative, the Mean Value Theorem, L'Hôpital's rules, and Taylor's Theorem, and apply them to solve problems in real analysis.
CO3: Understand the Riemann Integral, Riemann integrable functions, and the Fundamental Theorem of calculus, and apply these concepts to solve relevant problems in real analysis.
CO4: Develop proficiency in sequences and series of functions, including pointwise and uniform convergence, interchange of limits, and series of functions, and apply these concepts to study and solve problems in real analysis.
On completion of this course, the students will be able to
CO1: Develop a comprehensive understanding of complex numbers, including their properties, vectors, moduli, complex conjugates, exponential forms, arguments, roots of complex numbers, and regions in the complex plane.
CO2: Analyze and apply the concept of analytic functions, including limits, continuity, derivatives, Cauchy-Riemann equation, differentiability conditions, and examples of analytic functions. Understand elementary functions such as exponential, logarithmic, trigonometric, hyperbolic, inverse trigonometric, and hyperbolic functions.
CO3: Gain proficiency in integrals, including definite integrals of functions, contours, contour integrals, antiderivatives, Cauchy-Goursat theorem, simply and multiply connected domains, Cauchy's integral formula, Liouville's theorem, and the maximum modulus principle.
CO4: Demonstrate a strong understanding of series, including the convergence of sequences and series, Taylor's series, Taylor's theorem, and examples of Laurent's series. Analyze and apply residues and poles concepts, including isolated singular points, residues, Cauchy's residue theorem, and applications in evaluating improper integrals.
After the completion of this course the student will be able to
CO1: Demonstrate a solid understanding of graph theory, including definitions of graphs, vertex degrees, subgraphs, paths, cycles, and matrix representations of graphs.
CO2: Analyze trees, including their definitions, properties, bridges, spanning trees, cut vertices, and connectivity, and apply these concepts to solve problems related to Euler's tours, the Chinese postman problem, Hamiltonian graphs, and the traveling salesman problem.
CO3: Understand the concept of metric spaces, including their definitions and examples, open sets, closed sets, and the Cantor set, and apply these concepts to solve problems in metric spaces.
CO4: Develop proficiency in metric space concepts, including convergence, completeness, and continuous mapping, and apply Baire's theorem in metric spaces.
Upon completion of this course, students should be able to:
CO1: Fundamental Concepts of Matrices and Systems of Equations
Understand the basic algebraic properties of matrices. Apply matrices in various applications, including analytic geometry and difference equations. Demonstrate proficiency in solving systems of linear equations using elementary matrices, Gaussian elimination, and reduced row-echelon matrices.
Analyze the concepts of linear combinations of rows and columns, linear independence of columns, row equivalence, and rank of a matrix. Determine the normal form of matrices and identify consistent systems of equations.
CO2: Invertible Matrices and Vector Spaces
Define invertible matrices and explore the concept of left and right inverses. Understand the properties of orthogonal matrices. Analyze vector spaces, subspaces, linear combinations of vectors, spanning sets, and linear independence. Identify basis vectors and their significance in vector spaces.
CO3: Linear Mappings and Matrix Representations
Define linear transformations and understand their properties. Analyze the kernel and range of linear mappings. Determine the rank and nullity of linear mappings. Explore the concept of linear isomorphism.
Understand the matrix representation of linear mappings, including ordered bases and transition matrices. Identify nilpotent matrices and their index of nilpotency.
CO4: Eigenvalues and Eigenvectors
Understand the characteristic equation of matrices. Analyze algebraic multiplicities and geometric multiplicities of eigenvalues. Determine eigenspaces and eigenvectors.
Explore the concept of diagonalization and tri-diagonal matrices.Apply eigenvalues and eigenvectors in solving problems related to linear transformations and matrices.
MM6PRT01 : Project
CO1 Demonstrate library research skills in the area of mathematics
Critique mathematical presentations,
CO2 Produce a mature oral presentation of a non-trivial mathematical topic.