# Course Outcomes

Every subject in mathematics such as Calculus, Algebra, Linear Algebra, Discrete Mathematics, Ordinary Differential Equations, Numerical Methods, Mathematical and Statistical Techniques besides their subject specific outcomes has following underlying outcomes:

1. : Students should be able to effectively communicate mathematical concepts and solutions clearly and concisely using proper mathematical notation and terminology.
2. Students should be able to think critically and independently to solve complex problems and evaluate mathematical arguments.
3. Students should be able to reason logically and apply mathematical concepts to solve problems.
4. Students should be able to use mathematical software and graphing calculators to aid in the computation and visualization of mathematical concepts.

ODD SEMESTER

Mathematical and Statistical Techniques-I

The course outcomes of Mathematics and Statistical Techniques-I are:

• Shares and Mutual Funds: Students will be able to learn the concept of  shares, mutual funds and SIP, brokerage, rate of return and dividends.
• Permutation, Combinatorics and Linear Programming Problem: Students will develop the ability to calculate permutations and combinations using various techniques, such as the factorial notation, permutation formula, and combination formula. Students should be able to model and solve various business problems using mathematical techniques of linear programming,
• Summarization of Measures:Students should be able to describe and summarize business data using measures such as mean, median, mode, variance, and standard deviation.
• Elementary Probability Theory: Students should be able to apply probability and to calculate the probability of an event.
• Decision Theory: Students should be able to understand the fundamental concepts and principles of decision theory, including decision criteria.

Mathematics Paper-I (Calculus -I)

The course outcomes of Mathematics Paper-I (Calculus-I) are:

• Real Number System: Students should be able to understand real number system and their properties.
• Sequences: Students should have a strong understanding of fundamental concepts such as sequence, bounded sequences, limit of sequences, etc. Students should be able to define and identify sequences and understand the difference between finite and infinite sequences. Students should be able to determine if a sequence converges or diverges and calculate the limit of a convergent sequence. Students should be able to apply sequences in real-world problems such as compound interest, population growth, and finance.
• Solving first-degree and first-order differential equations: Students should be able to solve first-degree and first-order differential equations using various methods such as separation of variables, exact equations, and integrating factors. Students should be able to use differential equations to model real-world problems or problems in physics, biology, chemistry, and engineering and analyse the behaviour of systems.

Mathematics Paper-II (Algebra)

The course outcomes of Mathematics Paper-II (Algebra) are:

• Integers and Divisibility: Students should have a strong understanding of fundamental concepts such as prime numbers, divisibility, congruences, properties of integers, fundamental Theorem of Arithmetic and Number-theoretic functions.
• Functions, relations and binary operations: Students will learn the basic concepts of functions, relations, and binary operations, including domain, range, inverse, composition, equivalence relation, and binary operations.
• Polynomials: Students will develop skills in performing various polynomial operations, including addition, subtraction, multiplication, division, factor polynomials into simpler forms. Students will learn how to solve polynomial equations of various degrees, including quadratic equations, cubic equations, and higher-degree equations. Also, they will to extend the concept to complex number.

Mathematics Paper-I (Calculus -III)

Course outcomes of Mathematics Paper-I (Calculus-III) course:

• Infinite series: Students should be able to understand the concept of a series, the relationship between sequences and series, and be able to use different tests to determine the convergence or divergence of a series.
• Riemann Integration: Students will learn the definition of the Riemann integral, its properties and Cauchy’s Criteria.
• Applications of Integrations and Improper Integrals: Students will able to calculate the area between the curves, length of curve, etc. First and second fundamental theorems of Calculus. Students will learn the techniques of convergence and divergence of improper integrals, Gamma and Beta functions.

Mathematics Paper-II (Linear Algebra-I)

The course outcomes of Mathematics Paper-II (Linear Algebra-I)

• Systems of linear equation matrices: Students will be able to formulate/visualize/solve the equations of lines and planes. They will be able to identity types of matrices, invertible matrices and apply them to express system of linear equations in matrix form, perform elementary row operations, Gaussian elimination.
• Vector Spaces: Students should be able to identify and analyse vector space, linear span, linear independence and linear dependence, basis, dimension of a vector space, subspace, subspace test, properties of subspace.
• Determinants: Students should be able to understand the concept of a determinant and the properties that make it a useful tool to identify invertible matrices, to solve linear system.

Mathematics Paper-III (Ordinary Differential Equations)

The course outcomes of Mathematics Paper-II (Ordinary Differential Equations) are:

• Higher Order Linear Differential Equations: Students should have a firm grasp of what higher order linear ordinary differential equations are, how they are classified, and how to recognize them in various contexts and solution existence and unique. Students should be able to solve second-order ODEs using different techniques
• Systems of First Order Linear Differential Equations: Students will have developed skills to solve systems of first-order linear differential equations using various methods, including matrix methods, eigenvalues and eigenvectors.
• Numerical Solution of Ordinary Differential Equations: Developing skills to apply numerical methods, such as Euler’s method, improved Euler’s method, and Runge-Kutta methods, to solve first-order and first-degree differential equations.

EVEN SEMESTER

Mathematical and Statistical Techniques-II

The course outcomes of Mathematical and Statistical Techniques-II are:

• Functions, Derivatives and their Application: Students will be able to apply mathematical concepts to economics problems such as supply and demand analysis, production and cost analysis, and market equilibrium.
•  Interest and Annuity: Students should be able to apply mathematical concepts to financial problems such as compound interest, annuities, and present value calculations.
• Bivariate Linear Correlation and Regression: Students will be able to analyse the relation between to two variables.
• Time Series and Index Numbers: Students should be able to Analyze and interpret time series data using graphical and statistical methods, including trend analysis, seasonal analysis, and forecasting. Also to apply index number techniques to measure changes in prices, quantities, and other economic variables over time.
• Elementary Probability Distributions: Students should have a strong understanding of probability theory and its applications in business, including the use of probability distributions such as normal, binomial, and Poisson.

Mathematics Paper-I (Calculus -II)

The course outcomes of Mathematics Paper-I (Calculus-II) are:

• Limits and Continuity: Student will learn the concept of limit, continuity and their properties.
• Differentiability of functions: Students will understand differentiability concept, chain rule, higher order derivatives, Leibnitz’s rule, etc.
• Applications of Differentiability: Students will able to apply Rolle’s theorem, mean value theorem, L’Hospital rule, interpretation of first derivative, Second derivative test, sketching of graphs techniques, Taylor’s theorem.

Mathematics Paper-II (Discrete Mathematics)

The course outcomes of Mathematics Paper-II (Discrete Mathematics) are:

• Preliminary Counting: Students should have a strong understanding of countable sets, uncountable sets, addition and multiplication principles, partition, pigeonholes principle, etc.
• Advanced Counting: Students should be able to count and analyse the number of ways to arrange, select, and distribute objects and understand fundamental concepts such as permutations, combinations, multi sets, binomial and multinomial theorem, integer solution of equation.
• Recurrence Relation and Permutation: Students are expected to be able to formulate and solve recurrence relations of various types and analyze the behaviour of the sequences generated by them. Students are expected to be able to understand the basic concepts of permutations, compute the number of permutations of a set, and solve problems involving permutations

Mathematics Paper-I (Multivariable Calculus -I)

The course outcomes of Mathematics Paper-I (Multivariable Calculus-I) are:

• Functions of Several Variables: Understanding the nth-dimensional coordinate system, sequences in nth-dimensional, limit of a functions, compute partial derivatives, directional derivatives, and gradients of functions of several variables.
• Differentiation of a scalar fields: Students should be able to compute the total derivative, properties of differentiability, gradient and its properties and mixed partial derivatives.
• Applications of Differentiation of Scalar Fields and Differentiation of Vector Fields: Students should be able to calculate the rate of change of a scalar field, Taylor series, maxima and minima and other related aspects

Mathematics Paper-II (Linear Algebra-II)

The course outcomes of Mathematics paper-II( Linear Algebra-II) are

• Linear Transformation: Students should be able to define and explain what a linear transformation is, and understand the properties that make a transformation linear. Students should be able find associated matrix of linear transformation
• Inner Product Spaces: Students should be able to define, identify and execute what a inner product is, and communicate the properties associated properties, norms, Euclidean space, Gram Schmidt orthogonal process, etc.
• Eigenvalues, Eigenvectors and Diagonalizations: Students should be able to define and compute eigenvalues and eigenvectors of matrices in using characteristic polynomials. Students should be able to understand the properties of eigenvalues and eigenvectors, including how they can be used to diagonalize matrices. Students should be able to diagonalize matrices and understand the conditions under which a matrix is diagonalizable.

Mathematics Paper-III (Numerical Methods)

The course outcomes of Mathematics Paper-II (Numerical Methods) are:

• Solutions of algebraic and transcendental equations: Students should be able to define and differentiate between algebraic and transcendental equations, understand the properties of their solutions, and identify the types of equations. Students should be able to apply various methods to find solutions to algebraic and transcendental equations, including analytical, numerical, and graphical methods and understand the convergence of solution concepts.
• Interpolation, Curve fitting, Numerical integration: Students should be able to define, differentiate and apply between interpolation and curve fitting methods, understand the properties of numerical integration methods, and identify the types of equations and functions used in these methods
• Solutions of linear system of Equations and eigen value problems: Students should be able to apply various methods to solve linear systems of equations including Jacobi’s Method, Gauss Seidel Method, LU decomposition (Doolittle’s and Crout’s Method), etc. Also, students will able to compute the eigenvalues problems using Jacobi method