Semester |
Course code |
Course title |
Course outcomes |
I (core) |
MM 1141 |
Methods of Mathematics |
CO 1: Understanding the concepts of fundamental methods of solving problems like limit, continuity and differentiation
CO 2: Finding absolute maximum and minimum of functions
CO 3: Understanding application of extrema problems to Economics
CO 4: Understanding various Integration Techniques
CO 5: Finding Area under a curve through integration, work done, Pappu‟s Theorem and understanding the concept of hyperbolic functions and their applications |
I (compl) |
MM 1131.1 |
Calculus with applications in Physics-I |
CO 1: Understands the special points of a function, curvature and applies Rolle‟s Theorem and Mean value theorem on functions
CO 2: Understands integration by parts and reduction formula
CO 3: Understands the concept of infinite and improper integrals
CO 4: Applies the integration techniques to evaluate the area, volume etc
CO 5: Understands various types of Series such as arithmetic series, geometric series, the difference method, series involving natural numbers and transformation of series
CO 6: Understands Convergence of infinite series (Absolute and conditional convergence) and series containing only real positive terms; alternating series test
CO 7: Understands Operations with series (Sum and product) Convergence of power series and Taylor series
CO 9: Understands Scalars and vectors, Addition and subtraction of vectors, Multiplication by a scalar, Basis vectors and components, Magnitude of a vector, Multiplication of vectors
CO 10: Understands Equations of lines, planes and spheres, using vectors to find distances from Point to line; point to plane; line to line and line to plane |
I (compl) |
MM 1131.2 |
Calculus with applications in Chemistry I |
CO 1: Understands the special points of a function, curvature and applies Rolle‟s Theorem and Mean value theorem on functions
CO 2: Understands the Basic operations of complex numbers, modulus and argument; multiplication; complex conjugate, Polar representation of complex numbers and de Moivers theorem
CO 3: Understands the trigonometric identities and finding the nth roots of unity; solving polynomial equations, Complex logarithms and complex powers,
CO 4: Applies the complex numbers to differentiation and integration, Definition of hyperbolic and trigonometric analogies; identities of hyperbolic functions; solving hyperbolic equations; inverses of hyperbolic functions; calculus of hyperbolic functions
CO 5: Understands Scalars and vectors, Addition and subtraction of vectors, Multiplication by a scalar, Basis vectors and components, Magnitude of a vector, Multiplication of vectors
CO 6: Understands Equations of lines, planes and spheres, using vectors to find distances from Point to line; point to plane; line to line and line to plane
CO 7: Understands integration by parts and reduction formula
CO 8: Understands the concept of infinite and improper integrals
CO 9: Applies the integration techniques to evaluate the area, volume etc |
I (compl) |
MM 1131.3 |
Algebra, Geometry and Trigonometry |
CO 1: Understands preliminary algebra including calculators, algebraic expressions, quadratic equations, etc.
CO 2: Understands plane geometry – lines and angles, circles, triangles, straight line, ellipse, etc.
CO 3: Understands basic trigonometric functions, vectors and oblique triangles, law of sines, etc. |
II (core) |
Mm 1221 |
Foundations of Mathematics |
CO 1: Understanding the concepts of sets, functions and the way in which a mathematician formally makes statements and proves or disproves it
CO 2: Visualize some of the properties of graphs of elementary functions
CO 3: Understanding foundations of co-ordinate geometry
CO 4: Understand the application of polar coordinates in Astronomy
CO 5: Understanding three-dimensional rectangular co-ordinate system and basic operations on vectors |
II (compl) |
MM 1231.1 |
Calculus with applications in Physics-II |
CO 1: Apply Integral calculus and vectors to problems in chemistry
CO 2: Use integration to find the area and volume of a surface of revolution
CO 3: Evaluate multiple integrals
CO 4: Solving first order and second order linear differential equations
CO 5: Identify the Equations of different types of conics in Cartesian and polar coordinates and sketch them |
II (compl) |
MM 1231.2 |
Calculus with applications in Chemistry II |
CO 1: Understands the total differential and total derivative, Exact and inexact differentials, theorems of partial differentiation,
CO 2: Understands the chain rule, Change of variables, Taylors theorem for many-variable functions
CO 3: Understands the Stationary values of many-variable functions, Stationary values under constraints
CO 4: Understands various types of Series such as arithmetic series, geometric series, the difference method, series involving natural numbers and transformation of series
CO 5: Understands Convergence of infinite series (Absolute and conditional convergence) and series containing only real positive terms; alternating series test
CO 6: Understands Operations with series (Sum and product) Convergence of power series and Taylor series
CO 7: Understands the Differentiation of vectors, Integration of vectors, Space curves, Vector functions of several arguments, Surfaces, Scalar and vector fields
CO 8: Gets the knowledge of Vector operators like Gradient, divergence and curl, Cylindrical and spherical polar coordinates
CO 9: Understands Double integrals, Triple integrals, Applications of multiple integrals (Areas and volumes), Change of variables in multiple integrals and properties of Jacobians |
II (compl) |
MM 1231.3 |
Calculus and Linear Algebra |
CO 1: Solve special types of first order equations
CO 2: Solve second order linear differential equation, homogeneous and non-homogeneous equation.
CO 3: Solve second order equations by operator method.
CO 4: Solve Euler, Cauchy and Legender equations
CO 5: Solve system of linear equations
CO 6: Compute the rank of a matrix |
III (core) |
MM 1341 |
Elementary Number Theory and calculus I |
CO 1: Understanding the fundamental facts in elementary Number Theory
CO 2: Understand the physical and geometrical interpretations of vectors.
CO 3: Explain more properties of curves in three-dimension space using the concepts of differentiability
CO 4: Visualizing functions of more than one variable, sketching, contours and level surface plotting
CO 5: Understanding limits and continuity of multivariable functions, partial derivatives and its geometrical interpretation
CO 6: Solving extremum problems with constraints using Lagrange multipliers |
III (compl) |
MM 1331.1 |
Calculus and Linear algebra |
CO 1: Solve special types of first order equations
CO 2: Solve second order linear differential equation, homogeneous and non-homogeneous equation.
CO 3: Solve second order equations by operator method.
CO 4: Solve Euler, Cauchy and Legender equations
CO 5: Solve system of linear equations
CO 6: Compute the rank of a matrix
CO 7: Determine whether a square matrix is diagonalizable and compute its diagonalization if it is
CO 8: Understand the relation between roots and coefficients of a polynomial and apply these relations to solve polynomial Equations
CO 9: Characterise roots of a polynomial.
CO 10: Calculate approximate roots of a polynomial equation using bisection and Newton Raphson method |
III (compl) |
MM 1331.2 |
Linear Algebra, Probability Theory and Numerical Methods |
CO 1: Understands row reduction of Matrices, Determinants, Cramer's rule for solving system of equations
CO 2: Understands vectors, lines and planes, linear combinations, linear functions, linear operators, linear dependence and independence, special matrices like Hermitian matrices
and formulas
CO 3: Understands linear vector spaces, eigen values and eigen vectors, diagonalizing matrices and applications of diagonalization
CO 4: Understands the Basics of statistics such as Sample Space, Probability Theorems, Methods of Counting Random Variables
CO 5: Understands the Continuous Distributions, Binomial Distribution, The Normal or Gaussian Distribution and the Poisson Distribution
CO 6: Understanding the Algebraic and transcendental equations Convergence of iteration schemes
CO 7: Solves the Simultaneous linear equations using Gaussian elimination, Gauss-Seidel iteration
CO 8: Evaluates integrals using Numerical integration techniques such as Trapezoidal rule
Simpsons rule; Gaussian integration; Monte Carlo methods
CO 9: Understands Finite differences, Differential equations; Taylor series solutions; prediction and correction; Runge-Kutta methods |
III (compl) |
MM 1331.3 |
Complex Numbers, Algebra and Calculus |
CO 1: Understands the algebra of Complex numbers, point representation and its vector and polar form
CO 2: Understands the concept of limit and continuity of functions of complex variable Prove the Cauchy-Riemann equations |
IV (core) |
MM 1441 |
Elementary Number Theory and calculus Ii |
CO 1: Defining the congruence relation and the congruence classes in integers
CO 2: Understanding Chinese remainder theorem and its applications
CO 3: Finding double and triple integrals and their applications
CO 4: Evaluating the integrals of vector valued functions
CO 5: Understanding the concept of Divergence Theorem, Gauss Law, Stoke‟s Theorem and its applications |
IV (compl) |
MM 1431.1 |
Complex Analysis, Special Functions and Probability Theory |
CO 1: Demonstrate accurate and efficient use of complex analysis techniques
CO 2: Apply problem-solving using complex analysis techniques applied to diverse situations in physics, engineering and other mathematical contexts
CO 3: Evaluate integrals using Cauchy‟s Residue integration method
CO 4: Understands the Factorial Function, the Gamma Function; Recursion Relation, the Gamma Function of Negative Numbers, some Important Formulas Involving Gamma Functions, Beta Functions, Beta Functions in Terms of Gamma Functions
CO 5: Understands the Basics of statistics such as Sample Space, Probability Theorems, Methods of Counting Random Variables
CO 6: Understands the Continuous Distributions, Binomial Distribution, The Normal or Gaussian Distribution and the Poisson Distribution |
IV (compl) |
MM 1431.2 |
Differential Equations, Vector Calculus and abstract Algebra |
CO 1: Understands the General form First-degree first order equations and solving using Separable-variable equations; exact equations; inexact equations, integrating factors; linear equations; homogeneous equations; isobaric equations; Bernoullis equation; solves Higher-degree first-order Clairaut‟s equation
CO 2: Solving Linear equations with constant coefficients; linear recurrence relations; Laplace transform method, Linear equations with variable coefficients such as The Legendre and Euler linear equations;
CO 3: Solves exact equations using partially known complementary function; variation of parameters; Green's functions; canonical form for second-order equations
CO 4: Solves general ordinary differential equations; non-linear exact equations; isobaric or homogeneous equations and solves equations homogeneous in x or y alone and equations having y = Aex as a solution
CO 5: Evaluate line, surface and volume integrals
CO 6: Acquire fundamental concept of Group theory
CO 7: Enhance capacity for mathematical reasoning
CO 8: Develop problem solving skill |
IV (compl) |
MM 1431.2 |
Basic Statistics and Differential Equations |
CO 1: Understands basic aspects of Statistics including probability and sample spaces, graphical representation of data, frequency distribution, measures of central tendency and dispersion
CO 2: Understands the General form First-degree first order equations and solving using Separable-variable equations; exact equations; inexact equations, integrating factors; linear equations; homogeneous equations; isobaric equations; Bernoullis equation; solves Higher-degree first-order Clairaut‟s equation |
V (core) |
MM 1541 |
Real Analysis-I |
CO 1: Understands the existence of irrational numbers
CO 2: States the completeness axiom of the reals and do simple calculations with suprema and infima of bounded sets
CO 3: Proving the uncountability of R
CO 4: calculate limits of sequences using the algebra of limits for sequences and the standard list of basic sequences, limits of sequences and to prove Bolzano Weierstrass theorem
CO 5: state various convergence tests for series (e.g. comparison test or the ratio test) and use them to detect convergence or divergence of series
CO 6: Understands abstract metric spaces
CO 7: Understands the construction of Cantor set
CO 8: Understands the open and closed sets in R and their complements
CO 9: Understands the compactness, open covers, perfect and connected sets in R
CO 10: Proves the Baire‟s Theorem |
V (core) |
MM 1542 |
Complex Analysis I |
CO 1: Understands the algebra of Complex numbers, point representation and its vector and polar form
CO 2: Understands the concept of limit and continuity of functions of complex variable Prove the Cauchy-Riemann equations
CO 3: Understanding polynomials and rational functions, the exponential, trigonometric, hyperbolic, the logarithmic functions and inverse trigonometric functions
CO 4: Gets the knowledge of contour integrals and proves Cauchy‟s Integral formula. Also discusses about its applications in evaluating integrals
CO 5: Understands the Bounds of Analytic functions |
V (core) |
MM 1543 |
Abstract Algebra – Group Theory |
CO 1: Acquire fundamental concept of Group theory
CO 2: Enhance capacity for mathematical reasoning
CO 3: Develop problem solving skill
CO 4: Students can connect the theory of groups to problems in other discipline
CO 5: Defining and analysing various permutation groups
CO 6: Understanding Cosets, Lagrange‟s theorem and fundamental theorem of Isomorphism
CO 7: Solve boundary value problem |
V (core) |
MM 1544 |
Differential Equations |
CO 1: Understands first order differential equations and various methods to solve them
CO 2: Understanding the existence and uniqueness of solutions theorem
CO 3: Understands second order differential equations and various methods to solve them |
V (core) |
MM 1545 |
Mathematics software- LATEX & Sage Math |
CO1: Enables to prepare a project report in Mathematics using LATEX
CO 2: Typesets a simple article, prepares a table, inserts figures in the document and adds bibliography
CO 3: Understands to start Sage Math, use Sage Math cloud
CO 4: Do simple calculations using Sage Math calculator and by basic functions
CO 5: Plots the graphs of simple functions
CO 6: Understands matrix algebra, defining functions, operations on polynomials, complex number arithmetic, differentiation of functions
CO7: Understands the concepts of combinatorics and number theory, vector calculus |
V (open course) |
MM 1551 |
Business Mathematics |
CO 1: Provides basic mathematics for finance – interest and discount calculations, depreciation, etc.
CO 2: Differentiation and their applications to Business and Economics
CO 3: Provides basic knowledge on index numbers – their types, applications and limitations |
VI (core) |
MM 1641 |
Real Analysis-II |
CO 1: State the definition of continuous functions and verify or disprove this in easy examples, formulate characterizations of continuity in terms of convergent sequences.
CO 2: State the intermediate value theorem and the boundedness theorem and apply them to solve equations.
CO 3: State the definition of differentiable functions and to verify or disprove this in easy examples.
CO 4: Calculate derivatives using the chain rule, the algebra of differentiable functions and the rule on derivatives of compositional inverses.
CO 5: State Rolle's theorem, the Mean Value Theorem and L'Hospital's Rule and to apply them to recognise the shape of functions (e.g. existence of local extrema, subjectivity of
the derivative) and to calculate limits.
CO 6: State the definition of Riemann Integrability and derive the Cachy criteria.
CO 7: Establish the integrability using various results, like squeeze theorem, integrability of monotone functions etc.
CO 8: Derive the relation between integration and differentiation via fundamental theorem of calculus. |
VI (core) |
MM 1642 |
Complex Analysis II |
CO 1: Compute the Taylor and Laurent expansions of simple functions, determining the nature of the singularities
CO 2: Understands about the point at infinity
CO 3: Prove the Cauchy Residue Theorem and use it to evaluate improper integrals
CO 4: Understands the geometric considerations of conformal mapping
CO 5: Gets the knowledge of Mobius Transformations |
VI (core) |
MM 1643 |
Abstract Algebra – Ring Theory |
CO 1: Explain fundamental concepts of homomorphism of Groups
CO 2: Develop the notion of Ring theory
CO 3: Handle Factor ring
CO 4: Use the theory of rings to problems in other discipline |
VI (core) |
MM 1644 |
Linear Algebra |
CO 1: Understands the basics of Linear Algebra and matrix theory through geometry
CO 2: Demonstrate understanding of linear independence, span, and basis.
CO 3: Determine eigenvalues and eigenvectors and solve eigenvalue problems
CO 4: Apply principles of matrix algebra to linear transformations |
VI (core) |
MM 1645 |
Integral Transforms |
CO 1: Understands Laplace Transforms and its properties
CO 2: Understands its applications to Non- homogeneous Linear ODE
CO 3: Understands the Fourier series representation of periodic functions, odd and even functions, Half range expansions
CO 4: Understands Fourier integrals and its properties
CO 5: Understands Fourier Transform and its properties |
VI (core) |
MM 1661.1 |
Graph Theory |
CO 1: Understands the Fundamental Concepts of graph
CO 2: Understands the trees and Connectedness of graphs
CO 3: Understands Euler tours and Hamiltonian cycles
CO 4: Understands the concept of Chinese postman problem, Travelling salesman problem
CO 5: Understands the idea of planar graphs
CO 6: Gets the knowledge of Platonic bodies and Kuratowski‟s Theorem |
VI (core) |
MM 1646 |
Project |
CO 1: Computational understanding of mathematics to a broad understanding encompassing logical reasoning, generalization, abstraction, and formal proof.
CO 2: Create and verify their own conjectures, rather than simply using provided formulas, rules and theorems in multiple courses throughout the mathematics curriculum.
CO 3: Construct clear and well-supported mathematical arguments to explain mathematical problems, topics, and ideas in writing. |