I Semester- MAT 1.1 

Matrices, Differential calculus, Integral calculus, Theory of equations

• Relate an augmented matrix to a system of linear equations.

• Apply the Cayley-Hamilton Theorem to compute powers of a given square matrix.

• Compute limits, derivatives, and definite and indefinite integrals of algebraic, logarithmic, and exponential functions.

• Compute definite and indefinite integrals of algebraic and trigonometric functions using formulas and substitution.

• Applied to solve higher-degree polynomials.

• Use mathematical ideas to model real-world problems.

• Utilise technology to address mathematical ideas.

• Demonstrate the effective use of mathematical skills to solve quantitative problems in a wide array of authentic contexts.

• Demonstrate the ability to make rigorous mathematical arguments in axiomatic and non-axiomatic systems.

• Demonstrate effective written communication of mathematical concepts.

II Semester – MAT 2.1

Groups, Differential Calculus, Integral Calculus, Differential equations-I

• Construct and describe groups. They will learn the basic properties of groups and become familiar with important classes of groups. They will understand the crucial concept of simple groups.

• Use technological tools such as computer algebra systems of graphing calculators for visualisation and calculation of multivariable calculus concepts.

• Develop the ability to apply differential equations to significant applied and/or theoretical problems.

III Semester – MAT 3.1

Groups, Sequences and Series of Real Numbers, Differential Calculus

• Understand the proof, statement, and simple uses of Lagrange’s Theorem.

• Recognise the embedded infinite geometric series in geometric applications.

• Understand the consequences of the intermediate value theorem for continuous functions.

IV Semester – MAT 4.1

Groups, Fourier series, Mathematical Methods-I, Differential Equations-II

• Demonstrate familiarity with permutation groups and be able to decompose permutations into 2-cycles. Familiar with Fourier series and their applications, and be notionally aware of their convergence.

• Laplace transforms are used to simplify calculations in system modelling.

• Demonstrate an understanding of solution techniques for second- and higher-order differential equations; be familiar with qualitative tools for linear equation applications.

V Semester – MAT5.1

Rings, Integral domains, Fields, Vector Differential calculus,

Numerical methods-I

• Demonstrate familiarity with some of the applications of algebra to other fields, e.g., cryptography.

• Apply derivative concepts to find tangent lines to level curves and to solve optimisation problems.

• Analyse the error inherent in any such numerical approximation.

MAT5.2

Calculus of variation, Line and multiple integral, Integral theorems

• Compute the curl and the divergence of the vector field.

• Apply triple integrals to find volumes and the centre of mass.

• Compute the area of parametric surfaces in 3-dimensional space.

VI Semester – MAT 6.1

Linear algebra, PDE

• Compute inner products and determine orthogonality in vector spaces, including Gram-Schmidt orthogonalization.

• Be familiar with the modelling assumptions and derivations that lead to PDEs.

MAT6.2

Complex analysis, Numerical methods-II

• Applications in many scientific areas, including signal processing, control theory, electromagnetism, etc.

• Implement a variety of numerical algorithms using appropriate technology.