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Course Code    : AMAT 31303

Title                   :  Mathematics for Finance I

Pre-requisites   : PMAT 21272

Learning outcomes :

At the end of the course candidate will be able to

• define time value of money
• calculate present and future values of annuities and cash flows
• construct an investment portfolio to match present value and duration of a set of liability cash flows
• define basic types of financial derivatives
• identify appropriate derivative position for given investment circumstances
• evaluate the payoff and profit of basic derivative contracts
• apply put-call parity to identify arbitrage opportunities

 Course Contents:

Interest Theory: Time Value of Money: simple, compound Interest, comparing simple and compound interest, accumulation function, future value, current value, present value, net present value, discounting discount factor, rate of discount, interest payable monthly, quarterly, etc., nominal rate, effective rate, inflation and real rate of interest, force of interest, equation of value.

Annuities/cash flows: Annuity-immediate, annuity due, perpetuity, payable monthly or payable continuously, level payment annuity, arithmetic increasing/decreasing annuity, geometric increasing/decreasing annuity, term of annuity.

Loans: Principal, interest, term of loan, outstanding balance, final payment (drop payment, balloon payment), amortization, sinking fund.

Bonds: Price, book value, amortization of premium, accumulation of discount, redemption value, par value/face value, yield rate, coupon, coupon rate, term of bond, callable/non-callable.

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, margin, 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, properties of stock options, factors affecting option prices, assumptions and notations, 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.

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

 Assessment :  Based on tutorials, quizzes, mid-term tests and end of course examination

 Recommended Readings:

1. Kellison, S. (3 rd Ed., 2008). The Theory of Interest, McGraw-Hill/Irwin.

2. Hull, J.C. (10th Ed., 2018). Options, Futures and Other Derivatives, Pearson.

3. McDonald, R.L. (3 rd Ed., 2013). Derivatives Markets, Addison Wesley.

4. Kosowski, R. & Neftci, S.N. (3 rd Ed., 2015). Principles of Financial Engineering, Academic Press

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Course Code    : AMAT 22282

Title                 : Numerical Methods II

Pre-requisites   : AMAT 12253

Learning Outcomes:

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

1. define vector norm, matrix norm, and their general properties
2. use numerical methods for differentiation and integration
3. find numerical solutions to a system of equations using iterative methods
4. calculate approximate solutions to ordinary differential equations using numerical methods
5. discuss the convergence and stability of the solution.

 Course Contents:

Numerical Linear Algebra: Vector Norms, Matrix norms, General properties of vector and matrix norms, norm
convergence.   

 Numerical Differentiation and Integration: Numerical differentiation, open and closed Newton-Cotes formulae,
Trapezoidal, Simpson’s 1/3 and 3/8 rules, Romberg integration method, Gaussian quadrature.

Solving Linear Systems of Equations (Iterative): Relative error bound, condition number, iterative and relaxation
methods: Jacobi, Gauss-Seidel methods and their convergence, Richardson, SOR Iterative methods. Conjugate
Gradient Method.

 Numerical Solutions of Ordinary Differential Equations: Explicit and Implicit numerical schemes, Taylor-
Series method, Picard’s method of successive approximations, Euler’s method, Heun’s method, Midpoint method,
Runge-Kutta methods, computation of error bound, stability of methods, predictor-corrector methods: Adams -
Moulton, Adams-Bashforth, Milne’s methods, global and local truncations errors.

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

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

 Recommended Reading : 

1. Burden, R.L., Faires, J.D, Burden, M.L. (10th Ed., 2016). Numerical Analysis, Cengage Learning.
2. Trefethen, L.N. & Bau, D. (1997). Numerical Linear Algebra, Philadelphia, USA.
3. Golub, H., Vanloan, C.F. (2013). Matrix computations, JHU Press.
4. Kreyszig, E. (10th Ed., 2010). Advanced Engineering Mathematics, John Wiley.
5. Sauer, T. (2012). Numerical Analysis, Pearson.
6. Epperson, J.F. (2013). An Introduction to Numerical Methods and Analysis, Wiley.
7. Faul, A.C. (2016). A Concise Introduction to Numerical Analysis, Chapman and Hall/CRC.

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Course Code    : AMAT 22292

Title                   : Scientific Computing using appropriate software II

Pre-requisites   : AMAT 21262

Co-requisites   : AMAT 22282

 Learning Outcomes:

On completion of this unit, the student should be able to

• develop computer programs for curve fitting applications
• use software environment for numerical integration and optimization
• define function files for solving linear systems of equations
• solve initial value problems numerically.

 Course Contents:

Curve Fitting: Linear Least-Squares Regression, Linearization of nonlinear relationships: exponential, power and Saturation Growth Rate models, interpolation, extrapolation, interpolation hazards: multiple curve fitting.

Numerical Integration: Trapezoidal, Simpson’s methods, Gauss quadrature.

Optimization: One-Dimensional optimization and multidimensional optimization.

Solving Linear Systems: Solving linear algebraic equations using the software, Direct methods: naive Gauss elimination, pivoting, Gauss Elimination as LU Factorization, Iterative methods: Jacobi method, Gauss-Seidel method, Richardson method, and SOR methods.

Initial-Value Problems: Euler’s method, Heun’s method, Midpoint method, Runge Kutta Methods, adaptive methods for solving initial value problems, comparison of described methods.

Appropriate built-in functions in the software environment for selected numerical methods.

 Method of Teaching and Learning: A combination of lectures and computer laboratory sessions.

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

 Recommended Reading                

1. C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, McGraw-Hill, (2017).
2. Jaan Kiusalaas, Numerical Methods in Engineering with MATLAB (3e), Cambridge University Press, 2015
3. R. Otto and J.P. Denier, An Introduction to Programming and Numerical Methods in MATLAB, Springer-Verlag London Limited 2005

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Course Code    : AMAT 21272

Title                   :  Mechanics II

Pre-requisites   : AMAT 11232

 Learning Outcomes : 

Upon successful completion of this course, the student should be able to

1. describe and derive the moment of inertia of rigid bodies
2. collect and organize the knowledge for solving problems in motion of lamina
3. describe, derive and apply Euler’s equation of motion
4. collect and organize a sound knowledge of Lagrangian approach to mechanics
5. determine the Lagrangian functions for a physical systems
6. describe and derive the Lagrange equation of motion for impulsive motion.

 Course Content  :

Rigid Body Motion: Rigid bodies, Moments and products of inertia, Principal axes, Equimomental systems,
Motion of a lamina, Instantaneous centre, Body and space centrodes, Uniplanar motion of a rigid body, Impulsive
motion, Euler’s equations of Motion.

Lagrangian Mechanics: Generalized coordinates, Lagrange’s equations of motion for elementary systems,
Constraint forces, Lagrange’s equation of motion for holonomic systems, Determination of holonomic constraint
forces, generalized force functions, Lagrange equations, Constants of motion in the Lagrangian formalism,
Lagrange equation of motion for impulsive motion.

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

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

 Recommended Reading:

1. Chorlton, F. (2nd Ed., 2019). Textbook of Dynamics, D. Van Nostrand.
2. Desloge, E.A. (1982). Classical Mechanics, John Wiley, New York.
3. Gignoux C & Silvestre-Brac, B. (2014). Solved Problems in Lagrangian and Hamiltonian Mechanics,
Springer Netherlands.
4. Goldstein, H. (2011). Classical Mechanics, Addison Wesley.
5. Kelley, J.D. & Leventhal, J.J. (2016). Problems in Classical and Quantum Mechanics: Extracting the
Underlying Concepts. Springer.
6. Ramsey, A.S. (1975). Dynamics, Parts I & II, Cambridge University Press