Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH114
Module Title: Discrete Mathematics
Module Level: Level 1
Module Credits: 5.00
Semester: SEM2
Originating Department: Mathematical Sciences
Pre-requisites: N/A

 Aims To provide an introduction to the world of discrete mathematics, in particular graph theory and combinatorics.To acquaint the students with the most common techniques used in combinatorics.To enable the students to identify which combinatorial structure is more suitable to study a given problem.To introduce students to the most important aspects of graph theory.
 Learning outcomes After completing this module students should be able 1.Count combinatorial objects and determine the cardinality of finite sets.2.Know how to compute various parameters of a given graph.3.Understand the foundations of Graph Theory and Combinatorics
 Method of teaching and learning This module will be delivered by a combination of formal lectures and tutorials.
 Syllabus 1. Permutations and Combinations. Finite probability.2. The pigeonhole principle and its applications.3. Partially ordered sets.4. Binomial and Multinomial theorem.5. The inclusion-exclusion principle and its applications.6. Recurrence relations and generating functions.7. Graph Theory. Degrees and degree sequences. Isomorphism and Reconstruction. Trees. Connectivity. Mengerâ€™s Theorem. Eulerian and Hamiltonian Graphs. Directed graphs. Matchings. Planarity. Vertex and Edge colouring. Ramsey Theorem
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 42 14 94 150

## Assessment

 Sequence Method % of Final Mark 1 Final Exam 90.00 2 Class Test 10.00
 Module Catalogue generated from SITS CUT-OFF: 8/24/2019 3:37:15 PM