User Rating: 5 / 5

Course code  :  PMAT 11212

Title               :  Mathematics for Computing I

 Learning outcomes:

 On completion of this course, the student should be able to:

1. apply rules of propositional, predicate logic and methods of proof
2. demonstrate working knowledge of sets, relations, and functions
3. identify the properties of a function
4. find the inverse of function
5. apply Boolean algebra in simplifying combinatorial circuits

 Course Content:

Propositional Logic: Propositions, Truth values, Logical connectives, Truth table, Tautology and Contradiction, Logical
equivalence, Algebra of propositions, Validity of an argument; Predicate Logic - Quantifiers, Nested quantifiers, Negation
of quantified statements, Validity of an argument with quantifiers; Methods of Proof - Informal idea of a theorem and a
proof, Converse, inverse and the contrapositive of a statement, Direct proof, Proof by contradiction, contrapositive,
exhaustion and cases, Disproving by counter-examples, Principle of mathematical induction (weak and strong form).
Sets: Set notations, sets of numbers, Subsets of the real numbers and interval notation, Operations on sets, Algebra of sets,
Set identities, Power set, Cartesian product of sets.

Relations: Equivalence relations and equivalence classes, Properties of equivalence classes, Partitioning of sets.

Functions: Function notations, Image, and pre-image, One-to-one and onto functions, Composition of functions, Inverse
Function, Image and inverse image of subsets under functions.

Boolean algebra:  Axioms of Boolean algebra and its properties, Correspondence between Boolean algebra and
combinatorial logic circuits, Simplifications of combinatorial logic circuits using Boolean algebra.

 Method of Teaching and Learning: Lectures, interactive classroom sessions, and case discussions

 Assessment: End of course unit examination, group assignment, mid-term examination, class attendance

 Recommended Reading:

1. Johnsonbaugh, R. (8th Ed., 2017). Discrete Mathematics, Pearson.
2. Rosen, K.H. & Krithivasan, K. (7th Ed., 2011). Discrete Mathematics and Its Applications, McGraw-hill.
3. Kreyzig, E. (8th Ed., 2006). Advanced Engineering Mathematics, Wiley Student Edition

User Rating: 4 / 5

Course code  :  PMAT 11223

Title               :  Discrete Mathematics I

Pre-requisites :  A/L Combined Mathematics

Learning Outcomes:

On successful completion of the course, the student should be able to;

1. apply rules of propositional, predicate logic and methods of proof
2. demonstrate working knowledge of sets
3. demonstrate an understanding of relations and functions and be able to determine their properties
4. define equivalence relations and equivalence classes
5. define composite function
6. explain the conditions for the existence of the inverse function
7. use the Boolean algebra to simplify complex logic expressions.

Course Contents:

Mathematical Logic: Propositional logic, Propositional equivalences, Predicates and quantifiers, Nested
quantifiers, Rules of inference, Arguments, Normal forms, Methods of proof, Mathematical induction, Strong
induction, Well ordering principle.

Sets: Set notations; Sets of numbers and intervals; Subsets and equal sets; Power set; Cartesian product of sets; Set
operations; Algebra of sets.

Boolean Algebra: Boolean expressions and Boolean functions, Identities of Boolean Algebra, Duality, Logic gates,
Combinations of gates, Examples of circuits, Minimization of circuits

Relations: Relations and their properties, Functions as relations, Relations on a set, Properties of Relations,
Combining relations, n-ary relations, Equivalence relations, Equivalence classes and partitions,
Partial Orderings.

Functions: Function notation; One-to-one and onto functions; Composition of functions, Inverse function.

 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. Johnsonbaugh, R. (8th Ed., 2017). Discrete Mathematics, Pearson.
2. Rosen, K.H. (8th Ed., 2018). Discrete Mathematics and Its Applications, McGraw-Hill.

User Rating: 3 / 5

Course code  :  PMAT 11232

Title               :  Matrix Algebra

Pre-requisites :  A/L Combined Mathematics

Learning Outcomes:

On successful completion of the course, the student should be able to;

1. demonstrate the knowledge in the fundamentals of matrix algebra
2. apply elementary row operations to a matrix to transform it into its row-echelon form and find the inverse
of a square matrix
3. develop system of linear equations and represent in matrix form and apply Gaussian and Gauss-Jordan
method to solve simultaneous equations
4. classify a system of linear equations into consistent (unique solution and infinitely many solutions) and
inconsistent systems
5. identify the determinant of a square matrix, evaluate determinant using co-factors and apply elementary
row and column operations to evaluate determinants
6. describe and apply Cramer’s rule to solve system of linear equations
7. develop system of linear equations related to real world problems
8. explain and compute eigenvectors and eigenvalues of a matrix.

Course Contents: 

Matrices: Algebra of matrices, Special types of matrices, Transpose of a matrix, Symmetric and skew-symmetric
matrices, Inverse of a square matrix; Elementary row and column operations, Elementary matrices and their
properties, Inverse matrices using Elementary row and column operations, Properties of Inverse matrices

System of Linear Equations: Matrix representation of System of Linear equations, Row echelon form of a matrix,
Gaussian and Gauss-Jordan Elimination, Solutions of System of Equations, Applications of System of Linear
Equations.

Determinant of a matrix: Expansion by co-factors, Determinants of Triangular matrices, Evaluation of
determinants by elementary row operations, Cramer’s rule, and other applications of determinants.

Eigenvalues and Eigenvectors: Eigenvalues and eigenvectors of a matrix and their properties

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. Larson, R. & Falvo, D.C. (8th Ed., 2016). Elementary Linear Algebra, Brooks Cole.
2. Andrilli, S. & Hecker, D. (5th Ed., 2016). Elementary Linear Algebra, Elsevier Science.
3. DeFranza, J. & Gagliardi, D. (2015). Introduction to Linear Algebra with Applications, Waveland Press.
4. Lay, D.C., Lay, S.R. & McDonald, J.J. (5th Ed., 2015). Linear Algebra and Its Applications, Pearson
5. Anton, H. & Rorers, C. (2014). Elementary Linear Algebra Applications, Wiley.

Course Code : AMAT 32633

Title : Mathematics for Finance II

Pre-requisites: AMAT 31603

Learning outcomes: On successfully completion of the course the student will be able to

1. define and recognize the definitions of the financial derivatives

2. calculate the option pricing on various underlying assets

3. solve Black-Scholes equation numerically

4. identify the Greeks and their use

5. identify Swap strategies

Course Contents:

Trading Strategies: Single option and stock, Spreads and Combinations, Box spreads, Butterfly spreads,

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.

Numerical Solutions to Black-Scholes Equation: Converting to parabolic type, Finite difference methods, FTCS, BTCS and Cranck-Nicholson Schemes for Black-Scholes Equation

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

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

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

Recommended Readings:

1. John C Hull, Options, Futures

2. McDonald, R.L., Derivatives Markets, Addison Wesley, 2013

3. Robert Kosowski, Salih N. Neftci, Principles of Financial Engineering, Academic Press, 2014