**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.

** **

**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.

**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.

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