## Department- Mathematics

The college became a first grade College, Mathematics was the first science subject in which a Degree course was offered.  A decade later, the BSc M.Sc.  Course was started.

DEPARTMENT OF MATHEMATICS

ProgrammeOutcomes, Programme Specific Outcomes and Course Outcomes of B.Sc. and M.Sc.programmes in Mathematics

 Department of Mathematics After successful completion of three year degree program in mathematics a student should be able to; Programme Outcome of B.Sc. Mathematics PO-1.Think in a critical manner. PO-2.Know when there is a need for information, to be able to identify, locate, evaluate, and effectively use that information for the issue or problem at hand. PO-3.Formulate and develop mathematical arguments in a logical manner. PO-4.Acquire good knowledge and understanding in advanced areas of mathematics and statistics, chosen by the student from the given courses. PO-5.Understand, formulate and use quantitative models arising in social science,business and other contexts. Course Outcomes B. Sc Mathematics First year Course Outcomes After completion of these courses students should be able to; Programme     Specific     Outcome     of                       B.Sc., Mathematics ALGEBRA AND TRIGONOMETRY paper code - 0798 PSO-1. Find rank of matrixTo calculate Eigen values, Eigen vectors and the characteristics equations of a matrix. PSO-2. Use Cayley Hamilton theorem for determination of inverse of a matrix. PSO-3.Apply Matrix method for solving homogeneous and nonhomogeneous  linear equation . PSO-4.Define subgroup, center, Normalizer of a subgroup. PSO-5.Prove Lagrange’s theorem ,Euler’s theorem and Fermats theorem PSO-6.Prove a group has no proper subgroup if it is cyclic group of prime order. PSO-7.Define homomorphism ,kernel ofa homomorphism,isomorphism.

 PSO-8.Prove Cayley’s theorem , the fundamental theorem of homomorphism for groups PSO-9.Define rings , zero divisors of a ring , integral domain , field and prove theorems Aapply De Moivres theorem Separate real and imaginary parts of different types of functions. Find Summation of series. CALCULUS Paper-II (Paper code - 0799) Programme     Specific     Outcome     of     B.Sc., Mathematics PSO-1.Define ε − δ definition of the limit of a function. PSO-2.Classification of discontinuities. Differentiability. PSO-3.Find Asymptotes curvature. PSO-4.Trace curves in Cartesian and polar coordinates. PSO-5.Evaluate Quadrature. Rectification. Volumes and surfaces of solids of revolution. PSO-6.Solve Equations in which the variables are separable. PSO-7.Solve Exact differential equations. PSO-8.Find solution of Linear differential equations with constant coefficients. PSO-9.Understand Linear differential equations of second order. PSO-10.Use Method of variation of parameters for determination of solution of differential equation of second order. PAPER – III VECTOR ANALYSIS AND GEOMETRY (paper code - 0800) PSO-1.Interpret Scalar and vector product of three and four vectors. PSO-2.Apply Gauss, Green, and Stokes Theorems in vector integration. PSO-3.Trace conies and polar equation of a conic. PSO-4.Understand Plane , Straight line Sphere cone and Cylinder. PSO-5.Understand Generating lines, Confocal Conicoids and Reduction of second degree equations. Programme Outcomes B. Sc Mathematics Second year Programme Outcomes After   completion   of   these           courses students should be able to; PAPER - I ADVANCED CALCULUS (Paper Code - 0848) PSO-1.Define and recognize the concept of metric spaces, open sets, closed sets, limit points, interior point. PSO-2.Define and Illustrate the concept of completeness PSO-3.Determine the continuity of a function   PSO-4.Test for convergence of a series.

 PSO-5.Understand Continuity, Sequential continuity, Properties of continuous functions, Uniform continuity and differentiability of a function. PSO-6.Find Limit and continuity of functions of two variables. PSO-7.Apply Euler's theorem on homogeneous functions, Taylor's theorem for functions of two variables and Jacobians. PSO-8.Find envelopes, Evolutes, Maxima, minima and saddle points of functions of two variables. PSO-9.Apply Beta and Gamma functions. PSO-10.Understand Double and triple integrals. PAPER - II DIFFERENTIAL EQUATIONS (Paper Code - 0849) PSO1 Find Series solutions of differential equations. PSO 2 Understand Power series method, Bessel and Legendre, Functions and their properties- convergence. PSO 3 Obtain Orthogonality of Bessel functions and Legendre polynomials. PSO 4 Understand Laplace Transformation and inverse Transformation. PSO 5 Use Solution of integral equations and systems of differential equations using the PSO 6 Laplace transformation. Solve Some special types of equations which can be solved easily by methods other than the general method, Charpit's general method of solution. PSO 7 Understand Classification of linear partial differential equations of second order, PSO 8 Homogeneous and non-homogeneous equations with constant coefficients. PSO  9 Understand    Calculus of Variations of fixed boundaries and Moving Boundaries. PAPER - III MECHANICS (Paper Code - 0850) PSO 1 Understand Analytical conditions of Equilibrium, Stable and unstable equilibrium, To describe virtual work and Centenary. PSO 2 Understand Forces in three dimensions, To solve problem based on Poinsot's central axis, Null lines and planes, Dynamics. PSO 3 Describe Simple harmonic motion, Elastic strings. PSO 4 Understand velocities and accelerations along radial and transverse directions, Projectile, Central orbits. PSO 5 Understand motion on smooth and rough plane curves. PSO 6 Understand Motion in a resisting medium, motion of particles of varying mass, motion of a particle in three dimensions, acceleration.

 Programme Outcomes B. Sc Mathematics Final year Programme Outcomes After   completion   of   these           courses students should be able to; PAPER - I (Paper Code-0898) ANALYSIS PSO 1 Test Convergence of series by using Abel's and Dirichlet's test. PSO 2 Multiplication of series and Double series. PSO 3 Find Fourier expansion of piecewise monotonic functions. PSO 4 Define Intergrability of continuous and monotonic functions. PSO 5 Understand The fundamental theorem of integral calculus. PSO 6 Define Improper integrals and test of convergence by Comparison tests. Abel's and Dirichlet's tests. PSO 7 Define derivability and integrability of an integral of a function of a parameter. PSO 8Understand Complex numbers as ordered pairs and Geometric representation of Complex numbers. PSO 9 Determine Analytic functions. PSO 10 Calculate Mobius transformations and Conformal mappings of complex function. PSO 11 Learn about basic idea of Separable, second countable and first countable spaces and Continuous functions. Learn the Extension theorem. PSO 12 Learn about basic idea of compactness, Connectedness, Components, Continuous functions and connected sets. PART - II (Paper Code-0899) ABSTRACT ALGEBRA PSO    1   Learn   about  basics   of   Group- Automorphisms,          inner             automorphism, Automorphism groups and their compu-tations. PSO 2 Understand Sylow's theorems, Sylow subgroup, Structure theorem for finite Abelian groups. PSO 3 Define Ring homomorphism. Ideals and Quotient Rings and Field of Quotients of an Integral Domain. PSO 4 Understand Modules, Submodules, Quotient modules, Homomorphism and PSO 5 Isomorphism theorems. Learn about basic ideas of vector spaces. PSO 6 Understand Linear span, linear dependence, independence and their basic properties. PSO 7 Learn about Existence theorem for bases. Define Quotient space and its dimension. PSO 8 Learn basics of Linear transformations

 and their representation as matrices. PSO 9 Find Eigenvalues and eigenvectors of a linear transformation. PSO 10 Learn basics of Inner Product Spaces. Understand Cauchy-Schwarz inequality. PSO11 Calculate Orthogonal vectors, Orthogonal Complements and Orthonormal sets. PSO 12 Understand Bessel's inequality for finite dimensional     spaces     and         Gram-Schmidt Orthogonalization process. PAPER - III - (OPTIONAL) (II)    DISCRETE    MATHEMATICS    (Paper Code-0901) PSO 1 Understand basics of Sets and Propositions. PSO 2 Learn about Mathematical Induction, Principle of Inclusion and exclusion. PSO 3 Learn about Computability, Formal Languages and grammar. PSO 4 Define Binary Relations, Equivalence Relations ,Partitions and Partial Order Relations. PSO 5 Understand Lattices, Chains, Antichains and Pigeon Hole Principle. PSO 6 Understand the terminology Graphs and Planar Graphs. PSO 7 Understand Eulerian Paths and Circuits. Travelling Salesman Problem and Planner Graphs.. PSO 8 Understand Equivalent Machines. Finite State Machines as Language Recognizers. PSO 9 Develop algorithm of Time Complexity. PSO 10 Understand Discrete Numeric Functions and Generating Functions. PSO 11 Learn Linear Recurrence Relations with Constant Coefficients. PSO 12 Understand Solution by the Method of Generating Functions. PSO 13 Learn about Lattices and Algebraic Structures. PSO 14 Define Boolean Lattices and Boolean Algebras. PSO 15 Design and Implementation of Digital Networks and Switching Circuits. Department of Mathematics M.Sc. After successful completion of two year/four semester degree program in mathematics a student should be able to; Programme Outcomes PO-1. Inculcate critical thinking to carry out scientific investigation objectively without being biased with preconceived notions. PO-2. Equip the student with skills to analyze problems, formulate an hypothesis, evaluate and validate results, and draw reasonable conclusions thereof.

 PO-3. Prepare students for pursuing research or careers in industry in mathematical sciences and allied fields PO-4. Imbibe effective scientific and/or technical communication in both oral and writing. PO-5. Continue to acquire relevant knowledge and skills appropriate to professional activities and demonstrate highest standards of ethical issues in mathematical sciences. PO-6. Create awareness to become an enlightened citizen with commitment to deliver one’s responsibilities within the scope of bestowed rights and privileges. Programme Outcomes M. Sc Mathematics Programme Outcomes After completion of these courses students should be able to; Programme Specific Outcomes   M.Sc./M.A. Course PSO-1. Understanding of the fundamental axioms in mathematics and capability of developing ideas based on them. PSO-2.Inculcate mathematical reasoning. PSO-3.Prepare and motivate students for research studies in mathematics and related fields. PSO-4. Provide knowledge of a wide range of mathematical techniques and application of mathematical methods/tools in other scientific and engineering domains. PSO-5.Provide advanced knowledge on topics in pure mathematics, empowering the students to pursue higher degrees at reputed academic institutions. PSO-6. Strong foundation on algebraic topology and representation theory which have strong links and application in theoretical physics, in particular string theory. PSO-7.Good understanding of number theory which can be used in modern online cryptographic technologies. PSO-8.Nurture problem solving skills, thinking, creativity through assignments, project work. PSO-9. Assist students in preparing (personal guidance, books) for competitive exams e.g. NET, GATE, etc.

### Mathematics Department Faculties

S NoFaculty PhotoFaculty NameQualificationDepartmentDesignationMobile No
1 Mr. Surendra Kumar MeharM.Sc., M.PhilMathematicsAssistant Professor9669408776