## 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 2021/22

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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Class tests, exams and assessment 1 2.00 2.00 Lecture 22 1.00 22.00 Tutorial 10 1.00 10.00 Private study hours 66.00 Total Contact hours 34.00 Total hours (100hr per 10 credits) 100.00

### Private study

Taught session preparation: 18 hours
Taught session follow-up: 18 hours
Self-directed study: 7 hours
Assessment activities: 23 hours

### Opportunities for Formative Feedback

Attendance and formative assessment

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Coursework 1 (Gradescope) 10.00 In-course Assessment Coursework 2 (Gradescope) 10.00 In-course Assessment Coursework 3 (Gradescope) 10.00 In-course Assessment Coursework 4 (Gradescope) 10.00 In-course Assessment Online Assessment 60.00 Total percentage (Assessment Coursework) 100.00

This module will be reassessed by an online time-constrained assessment.