BRIJ MOHAN

Course Objectives: To comprehend various computational techniques to find an approximate value for possible root(s) of non-algebraic equations and find the approximate solutions of a system of linear equations and ordinary differential equations system. Also, the use of a Computer Algebra System (CAS) by which the numerical problems can be solved both numerically and analytically to enhance problem-solving skills.

Course Learning Outcomes: The course will enable the students to:
i) Learn some numerical methods to find the zeroes of nonlinear functions of a single variable and the solution of a system of linear equations up to a certain given level of precision.
ii) Know about methods to solve linear equations, such as Gauss−Jacobi, Gauss−Seidel, and SOR methods.
iii) Interpolation techniques to compute the values for a tabulated function at points not in the table.
iv) Applications of numerical differentiation and integration to convert differential equations into difference equations for numerical solutions.

Course Objectives: This course introduces C++ programming in the idiom and context of mathematics and imparts a starting orientation using available mathematical libraries and their applications.

Course Learning Outcomes: On completing this paper, the student will be able to:

i) Understand and apply the programming concepts of C++, which is essential to mathematical investigation and problem-solving.
ii) Learn about structured data types in C++, learn about applications in the factorization of an integer, and understand Cartesian geometry and Pythagorean triples.
iii) Use of containers and templates in various applications in algebra.
iv) Use mathematical libraries for computational objectives.
v) Represent the outputs of programs visually in terms of well-formatted text and plots.

Course Objectives: This course helps the students to develop skills and knowledge of standard concepts in cryptography and demonstrates how cryptography plays an important role in the present digital world by knowing encryption and decryption techniques and secure data in transit across data networks.

Course Learning Outcomes: After the course, the student will be able to:

i) Understand the fundamentals of cryptography and computer security attacks.

ii) Learn about various ciphers and data encryption standard.
iii) Review basic concepts of number theory and finite fields.
iv) Learn about advanced encryption standard.
v) Understand the fundamentals of RSA and elliptic curve cryptography.
vi) Encrypt and decrypt messages using block ciphers, sign and verify messages using well known signature generation and verification algorithms.

Course Objectives: This course is an introduction to the application of mathematics in financial world, that enables the student to understand some computational and quantitative techniques required for working in the financial markets and actuarial mathematics.
Course Learning outcomes: On completion of this course, the student will be able to:

i) Know the basics of financial markets and derivatives including options and futures.

ii) Learn about pricing and hedging of options, as well as interest rate swaps.

iii) Learn about no-arbitrage pricing concept and types of options.

iv) Learn stochastic analysis (Ito formula, Ito integration) and the Black−Scholes model.

v) Understand the concepts of trading strategies and valuation of currency swaps.