## COMP1511 Introduction to Discrete Mathematics

### 10 creditsClass Size: 500

Module manager: Kristina Vuskovic
Email: k.vuskovic@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2022/23

This module is not approved as a discovery module

### Module summary

Discrete mathematics studies finite mathematical structures and is the mathematical foundation for many Computer Science disciplines including algorithm design, data structures, database theory, formal languages and automata, compilers and importantly security. This module concentrates on the fundamentals of discrete mathematics introducing a number of concepts and skills that will be applied throughout the remainder of the Computer Science curriculum.This module builds upon previously taught mathematics modules and introduces students to a variety of powerful tools that can model a wide range of problems that arise in many areas including transportation, telecommunications and molecular biology.

### Objectives

To develop the range of concepts and techniques that students have when approaching real world problems and to allow students the opportunity to apply problem solving techniques to problems that arise in Computer Science disciplines. To prepare students for further mathematical study in the discipline of Computer Science.

Learning outcomes
On successful completion of this module a student will have demonstrated the ability to:

- apply counting arguments to problems that arise in Computer Science and more widely.
- recall definitions and theorems from the topic areas of combinatorics, discrete probability and graph theory.
- construct mathematical arguments, in the effort to prove the correctness of theorems.
- deploy problem solving techniques to problems within the discipline.
- transfer problem solving skills into difference domains.

### Syllabus

This module covers the following 3 topic areas:

- Combinatorics : multiplication principle, addition principle, Pigeon hole principle, permutation and combinations (with and without repetition).
- Discrete probability : experiment, sample space, events, finite probability space, equi-probable spaces, conditional probability, mutually exclusive and independent events.
- Graph theory : graph models, graph isomorphism, degree, paths, cycles, Euler's theorem, bipartite graphs and trees.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Tutorial 10 1.00 10.00 Private study hours 68.00 Total Contact hours 32.00 Total hours (100hr per 10 credits) 100.00

### Opportunities for Formative Feedback

Attendance and formative assessment

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Coursework 1 5.00 In-course Assessment Coursework 2 5.00 In-course Assessment Coursework 3 5.00 In-course Assessment Coursework 4 5.00 Total percentage (Assessment Coursework) 20.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) (S1) 2 hr 80.00 Total percentage (Assessment Exams) 80.00

This module will be reassessed by examination only