Course code  :  PMAT 12242

Title               :  Discrete Mathematics II

Pre-requisites :  PMAT 11223

Learning Outcomes:

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

1. demonstrate knowledge of topics including divisibility, prime numbers, congruences and Diophantine
equations
2. understand the logic and methods behind the major proofs in Number Theory
3. apply various properties relating to the integers including the Well-Ordering Principle, primes, unique
factorization, the division algorithm, greatest common divisors, and modular arithmetic
4. understand and prove theorems/lemmas and relevant results in graph theory
5. apply the basic concepts of graph theory, including Eulerian trails, Hamiltonian cycles, bipartite graphs,
planar graphs, and Euler characteristics on solving problems
6. apply algorithms and theorems in graph theory in real-world applications
7. apply counting principles to solve problems.

 Course Contents:

Counting: Basic Principles of Counting, Pigeonhole Principle, Permutations and Combinations.
Number Theory: The Well Ordering Principle, Divisibility and Division Algorithm, The Greatest Common
Divisor, The Euclidean Algorithm, Prime Numbers, Infinitude of Primes, The fundamental theorem of arithmetic,
Linear Diophantine Equation, Modular Arithmetic: solving linear congruence.
Graph Theory: Graph Terminology, Special Types of Simple Graphs, Subgraphs, Euler Cycles, Hamiltonian
Cycles, Representations of Graphs, Graph Isomorphism, Planar Graphs, Kuratowski’s Theorem, Graph
Colouring.

 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., (8^th edition , 2017), Discrete Mathematics, Pearson.
2. Rosen, K.H., Krithivasan, K., (7^th edition, 2013), Discrete Mathematics and Its Applications, McGraw-Hill.
3. Rosen, K.H. (6th Ed., 2010). Elementary Number Theory and Its Applications, Pearson.