User Rating: 5 / 5

Course Unit Code     : AMAT  41833

Course Title               : Linear programming and Optimization

Pre-requisites            : PMAT 21553

Learning outcomes:

Upon successful completion of the course unit the student will be able to:

• develop a linear programming model from problem description,
• use the simplex method for solving linear programming problems,
• use the revised simplex method to solve linear programming problems,
• interpret the dual of a linear programming problem and solve the resulting dual problem using the dual simplex method,
• obtain the solution to the primal problem from the solution of the dual problem
• use methods of linear programming for solving assignment problems and transportation problems
• identify the convex functions
• solve optimization problems in various areas using linear and non-linear programming methods

 Course Content:

Optimization, Types of optimization problems,

Linear Programming: Formulate linear programming problem: Extreme Points, Basic Feasible Solutions, Solutions using graphical methods, Simplex method, Revised simplex method, Duality theory, Primal and dual problems, Reduction of linear inequalities, Hungarian method, Big m method.

Non Linear programming: Types of non-linear programing, Convex and concave functions, one variable unconstrained optimization, multivariable unconstrained optimization, Convex programming

Applications of Linear Programming Problems: Transportation problem and Assignment problem

Implement Linear programming problems using Excel

Method of Teaching and Learning:  A combination of lectures, group projects, case studies, tutorial discussions and presentations.

Assessment: Based on tutorials, group project, tests, presentations and end of course examination

Recommended Textbook:

1. David G. Luenberger, Linear and Nonlinear Programming, (4e) Springer; 2016
2. Jiri Matousek, Bernd Gärtner, Understanding and Using Linear Programming. Springer Berlin Heidelberg, 2009
3. F. S. Hillier and G. Lieberman, Introduction to Operations Research, McGraw-Hill, (10e). 2015

User Rating: 5 / 5

Course Code    : AMAT 41823

Title                   : Quantum Mechanics 

Pre-requisites   : AMAT 11513

 Learning Outcomes:

At the end of this course, the student should be able to

•  demonstrate knowledge of concepts and principles of quantum mechanics and to apply them to solve simple problems.

 Course Contents:

Quantum Mechanics:

Quantum mechanics in Hilbert space, Axiomatic structure of quantum mechanics, The Shrödinger picture, Heisenberg and interaction picture, Complete set of observables, formalism of wave mechanics and its applications, Completely continuous operators, uncertainty principle, potential well, simple harmonic oscillator, scattering theory of two particles, potential scattering, approximate methods

 Method of Teaching and Learning: A combination of lectures, tutorial discussions and presentations.

 Assessment: Based on tutorials, tests, presentations and end of course examination.

 Recommended Reading      :

1. Schiff, L.I., Quantum Mechanics (4e), McGraw-Hill India. (2014).
2. Prugovecki, E., Quantum Mechanics in Hilbert Space (2e), Courier Corporation, 2013
3. Liboff R, L., Introductory Quantum Mechanics, (4e) Pearson India (2011).
4. Baggot, J., The meaning of Quantum Theory, Oxford University Press. (1997).
5. Sakurai, J.J., Advanced Quantum Mechanics, Replica Press (P) LTD, India. (2013).

User Rating: 5 / 5

Course Code  :           AMAT 43976

Title                :           Research/Study Project

 Learning Outcomes:

At the end of this course, the student should be able to demonstrate competence in research/independent-study in an area in Applied Mathematics.

 Course Contents:

Undergraduate research project is an inquiry, investigation, or creation produced by a final year honours degree undergraduate that makes a contribution to the discipline and reaches beyond the traditional curriculum. Undergraduate research project is designed to provide students with the opportunity to develop and practice advanced discipline-specific projects in collaboration with senior academics in the department.

 Method of Teaching and Learning: A research/study project under the supervision of a senior staff member of the department.

Assessment: Submission of a research/study project report and an oral presentation.

Recommended Reading      : Required reading material will be recommended by the supervisor depending on the relevant project.

User Rating: 3 / 5

Course Code    : AMAT 41813

Title                   : Financial Mathematics

Pre-requisites   : PMAT 11522

Learning outcomes:

On successfully completion of the course the student will be able to

• define and recognize the definitions of the financial derivatives
• calculate the option pricing on various underlying assets
• solve Black-Scholes equation numerically
• identify the Greeks and their use
• identify Swap strategies

Course Content:

Time Value of Money: Simple and Compound Interest, accumulation function, future value, current value, present value, net present value, discount factor, discount rate (rate of discount), convertible monthly, nominal rate, effective rate, inflation and real rate of interest, force of interest, equation of value.

General Cash Flows and Portfolios: yield rate/rate of return, dollar-weighted rate of return, time weighted rate of return, current value, duration (Macaulay and modified), convexity (Macaulay and modified), portfolio, spot rate, forward rate, yield curve, stock price, stock dividend

Basic terms in Financial Markets: derivative, underlying asset, over the counter market, short selling, short position, long position, ask price, bid price, bid-ask spread, lease rate, stock index, spot price, net profit, payoff, credit risk, dividends, mmargin, maintenance margin, margin call, mark to market, no arbitrage, risk-averse, type of traders.

Options: call option, put option, expiration, expiration date, strike price/exercise price, European option, American option, Bermudan option, option writer, in-the-money, at-the-money, out-of-the-money, covered call, naked writing, put-call parity.

Forwards and Futures: forward contract, futures contract, outright purchase, fully leveraged purchase, prepaid forward contract, synthetic forwards, cost of carry, implied repo-rate.

Option Pricing: Binomial Trees: One, two or more binomial periods, Put and Call options, American options, Options on stock index, currencies and future contracts, Risk Neutral pricing, log normality.

The Black-Scholes Formula: Brownian motion, martingales, stochastic calculus, Ito processes, stochastic models of security prices, Black-Scholes Merton Model, Black-Scholes Pricing formula on call and put options, Applying formula to other assets.

Option Greeks: Definition of Greeks, Greek Measures for Portfolios.

Swaps: swap, swap term, prepaid swap, notional amount, swap spread, deferred swap, simple commodity swap, interest rate swap

 Assessment: Based on assignment, quizzes, group projects, mid-term test, and end of course examination.

 Recommended Readings:

1. John C Hull, Options, Futures and Other Derivatives (10e), Pearson, 2017
2.  McDonald, R.L., Derivatives Markets, Addison Wesley, 2013
3. Robert Kosowski, Salih N. Neftci, Principles of Financial Engineering, Academic Press, 2014