FOUR YEAR UNDER GRADUATE PROGRAM (FYUGP)

PROGRAM NAME: B.SC. MATHEMATICS (MAJOR)

PROGRAM OUTCOME

• Able to understand the fundamental concepts in mathematics and provided with sufficient knowledge and skills to be motivated towards research in mathematics and related fields. 

• Equipped with problem-solving skills, analytical thinking, abilities, and aptitudes to apply mathematical methods and ideas to solve real-life problems. 

• Enhance their employability for Govt. jobs, subsequent careers, and educational programmes.

COURSE OUTCOME 

SEM 1

Classical and Linear Algebra (UMATMAJ 11001): 

• Learn about complex numbers, different tools to find roots of an equation, inequalities.
• Know about consistent and inconsistent systems of linear equations, rank of a matrix, eigen values and eigen vectors.

Logic, Integers, and Boolean Algebra (UMATSEC 11001 – Theory and Practical):

• Understand the concept of logical operators, different types of proposition predicates, quantifiers, and logical equivalence.
• Become familiar with Boolean algebra, Karnaugh diagrams, switching circuits, and their applications.

SEM 2
Calculus and Geometry (UMATMAJ 12002):

• Know about higher order derivatives, L’Hospital’s rule and some applications of derivative and integration.
• Understand the basic concept of conics and its classification and properties of spheres, cylindrical surfaces, conicoids, paraboloids etc.

Graph Theory (UMATSEC 12002 – Theory and Practical):

• Understand the basics of graph, tree and its properties, Eulerian and Hamiltonian graphs
• Apply graph theory to find the shortest path using Dijkstra’s algorithm and can relate graph theory to real-world problems.

 

PROGRAM NAME: B.SC. MATHEMATICS (MINOR)

PROGRAM OUTCOME

• Students will be equipped with problem-solving skills, analytical thinking, abilities, and aptitudes.
• Recognise the importance and value of mathematical thinking, training and approache to problem solving on a diverse variety of disciplines.
• Enhance their employability for Govt. jobs, subsequent careers and educational programmes.

 COURSE OUTCOMES

SEM 1 & 2

Classical and Linear Algebra (UMATMIN 10001):

• Understand the concept of complex numbers, familiarize with some inequalities, solve the equations by different methods.
• Know about the rank of a matrix, eigen values and eigen vectors.

 

CHOICE BASED CREDIT SYSTEM (CBCS)

PROGRAM NAME: B.SC. MATHEMATICS (HONOURS)

PROGRAM OUTCOME

• Able to understand the fundamental concepts in mathematics and provided with sufficient knowledge and skills to be motivated towards research in mathematics and related fields.
• Equipped with mathematical modeling ability, problem-solving skills, creative talent and the power of communication necessary for various kinds of employment.
• Students will have a creative and logical mind by which they can analyze & solve practical problems in their lives.
• Students will create an interdisciplinary relationship between the other streams.
• Enabling students to develop a positive attitude towards mathematics as an interesting and valuable subject of study.

COURSE OUTCOMES

SEM 3

Theory of Real Functions and Introduction to Metric Space (CC5):

• Understand the concept of real-valued functions, limit, continuity, uniform continuity, differentiability and series expansion.
• Learn basic topology on metric space and their properties, convergence of sequence in metric space.

Group Theory-I (CC6):

• Know about the concept of groups, different types of groups and cosets.
• Learn about group homomorphism and its properties, fundamental isomorphism theorems and able to solve related problems of homomorphism and isomorphism.

Riemann Integration and Series of Functions (CC7):

• Understand basic knowledge of Riemann integration of a function and convergence of an Improper integral
• Know about point wise and uniform convergence of sequence and series of function, different theorems on Power series and Fourier series. 

Logic and Sets (SEC1):

• Understand the concept of logical operators, different types of proposition, predicates, quantifiers, logical equivalence, binding variables.
• Know about partial order relations, cardinal numbers, well ordered sets and related results. 

Calculus, Geometry and Differential Equation (GE3):

• Know about higher order derivatives, L’Hospital’s rule and some applications of derivative and integration.
• Understand the basic concept of conics and its classification and properties of spheres, cylindrical surfaces, conicoids, paraboloids etc.

SEM 4

Multivariate Calculus (CC8):

• Know about limit and continuity of functions of two or more variables, partial derivatives, differentiability, Chain rule, directional derivatives, tangent planes etc.
• Able to solve constrained optimization problem, evaluate double and triple integral, line integrals etc. 

Ring Theory and Linear Algebra -I (CC9):

• Know about the concept of ring, ideals, integral domains and fields, isomorphism of rings.
• Know about the vector spaces, subspaces, linear transformation and matrix representation of a matrix. 

Metric Spaces and Complex Analysis (CC10):

• Understand the topological properties in a metric space, continuity and homeomorphisms.
• Know about the stereographic projection, differentiability and analyticity of complex functions, evaluation of contour integrals, series expansions of analytic functions. 

C Programming Language (SEC 2--Theory):

• Understand the concept of compiler, machine language, programming language and importance of C Programming, Operators in C.
• Know about the use of Statemants, Arrays, mathematical libraries for C languages. 

Algebra (GE4):

• Learn about complex numbers, different tools to find roots of an equation, inequalities.
• Know about consistent and inconsistent systems of linear equations, rank of a matrix, eigen values and eigen vectors.

SEM 5

Group Theory II (CC11):

• Gain a clear concept of Groups Automorphism, external and internal direct product of groups, Group action etc.
• Understand the Cayley’s theorem, Index theorem and Sylow’s theorem, Simplicity and non-simplicity test. 

Numerical Methods (CC12 – Theory and Practical):

• Know about the different types of errors, interpolation method, numerical differentiation, numerical integration.
• Know different numerical methods to find the solution of equations, ODE, system of linear equations with practical using C language.

Probability and Statistics (DSE1):

• Know about the basic concept of probability theory, distributions, mathematical expectation etc.
• Know about the basic concept of Sampling distributions, estimation of parameters, statistical hypothesis and its applications. 

Number Theory (DSE2):

• Know the basic concept of Euclidean Algorithm, Linear Diophantine Equations, Gaussian integers.
• Understand about linear congruences and primitive roots, Legendre symbol and Fermat’s two square theorem.

SEM 6

Ring Theory & Linear Algebra-II (CC13):

• Know about Polynomial rings, principal ideal domains, integral domain, irreducibility, primes, Euclidean domain, Unique factorization domain.
• Understand the concept of dual spaces, dual basis, double dual, Inner product spaces and orthogonal complements, Normal & self-adjoint Operator. 

Partial Differential Equations & Applications (CC14):

• Know the basic concepts of PDE, Canonical forms, heat equation, wave equation and Laplace equation, Classification of second order linear equations.
• Know about Cauchy problem, Constrained motion, modelling ballistics and planetary motion, Kepler's second law & its applications. 

Linear Programming (DSE3):

• Understand the idea of B.F.S., Convex sets, simplex method, Big-M Method, Two phase method and duality.
• Understand the idea of transportation and assignment problems, basic idea of game theory. 

Boolean Algebra and Automata Theory (DSE4):

• Understand duality principle, lattices as ordered sets, lattices, products and homomorphisms, of modular and distributive lattices
• Know about Boolean algebra, Karnaugh diagrams, Logic gates, switching circuits, basic concept of automata theory.

CHOICE BASED CREDIT SYSTEM (CBCS)

PROGRAM NAME: B.SC. MATHEMATICS (PROGRAM)

PROGRAM OUTCOME

• Equipped with mathematical modeling ability, problem-solving skills and the power of communication necessary for various kinds of employment.
• Students will have a creative and logical mind by which they can analyze & solve practical problems in their lives.
• Students will create an interdisciplinary relationship between the other streams.
• Enabling students to develop a positive attitude towards mathematics as an interesting and valuable subject of study.

COURSE OUTCOMES

SEM 3

Algebra (DSC3):

• Learn about complex numbers, different tools to find roots of an equation, inequalities.
• Know about consistent and inconsistent systems of linear equations, rank of a matrix, eigen values and eigen vectors. 

Logic and Sets (SEC1P1):

• Understand the concept of logical operators, different types of proposition, predicates, quantifiers, logical equivalence, binding variables.
• Know about partial order relations, cardinal numbers, well ordered sets and related results.

SEM 4

Differential Equations and Vector Calculus (DSC4):

• Know about wronskian, solving linear homogeneous and non-homogeneous equations of higher order, ordinary and singular points of an ODE, phase plane.
• Gain idea of vector triple product, limit and continuity of vector functions, differentiation and integration of vector functions. 

Theory of Equations (SEC1P2):

• Know the concept of polynomial, relation between roots and coefficient of an equations, symmetric functions,
• Know the solution of cubic, biquadratic equation and reciprocal equation, separation of real roots by strum’s theorem.

SEM 5

Group Theory and Linear Algebra (DSEP1):

• Know about various groups like alternating group, dihedral group, matrix group, Klein’s 4 group, symmetric group, Permutation group etc.
• Understand the concept of vector space, basis and dimension, Linear Transformation and matrix representation and its properties, Isomorphisms. 

Theory of Probability (SEC2P1):

• Know about the basic concept of probability theory, distributions, mathematical expectation etc.
• Know about the basic concept of regression, correlation coefficient, law of large numbers etc.

SEM 6

Linear Programming (DSEP2):

• Understand the idea of B.F.S., Convex sets, simplex method, Big-M Method, Two phase method and duality.
• Understand the idea of transportation and assignment problems, basic idea of game theory. 

Boolean Algebra and Automata Theory (SEC2P2):

• Understand duality principle, lattices as ordered sets, lattices, products and homomorphisms, of modular and distributive lattices
• Know about Boolean algebra, Karnaugh diagrams, Logic gates, switching circuits, basic concept of automata theory.