# CS137-12 Discrete Mathematics & its Applications 2

Academic year
21/22
Department
Computer Science
Level
Undergraduate Level 1
Module leader
Ramanujan Maadapuzhi Sridharan
Credit value
12
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry

##### Introductory description

This module is designed to introduce students to language and methods of the area of Discrete Mathematics.

##### Module aims

The focus of the module is on basic mathematical concepts in discrete maths and on applications of discrete mathematics in algorithms and data structures. One of the aims will be to show students how discrete mathematics can be used in modem computer science (with the focus on algorithmic applications).

##### Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Introduction to combinatorics: counting techniques, pigeonhole principle, inclusion-exclusion.
Recurrence relations, solving recurrences using generating functions.
Master Theorem for solving recurrences.
Graphs. Basic graph algorithms. Trees. Applications of graphs.
Applications of linear algebra and matrix algebra in algorithms (e.g., in web searching).
Algorithmic applications of random processes and Markov chains, for example, cover time in graphs and card shuffling.
Partitions, enumerations with symmetries.

##### Learning outcomes

By the end of the module, students should be able to:

• - Understand the notion of mathematical thinking, mathematical proofs, and algorithmic thinking, and be able to apply them in problem solving.
• - Understand the basics of discrete probability and number theory, and be able to apply the methods from these subjects in problem solving.
• - Use effectively algebraic techniques to analyse basic discrete structures and algorithms.
• - Understand asymptotic notation, its significance, and be able to use it to analyse asymptotic performance for some basic algorithmic examples.
• - Understand some basic properties of graphs and related discrete structures, and be able to relate these to practical examples.
##### Indicative reading list

Please see Talis Aspire link for most up to date list.

##### Subject specific skills

Basic knowledge of graph theory and its applications in algorithms
Basic knowledge of discrete probability and its applications in algorithms
Understanding and using asymptotic notations in design and analysis of algorithms

##### Transferable skills

Communication - Reading and writing mathematical proofs
Critical thinking - problem solving
Technical - Technological competence and staying current with knowledge

## Study time

Type Required
Lectures 30 sessions of 1 hour (21%)
Seminars 9 sessions of 1 hour (6%)
Private study 81 hours (58%)
Assessment 20 hours (14%)
Total 140 hours
##### Private study description

Revision of lectures
Going through the problems solved during seminar sessions
Solving past exam papers

## Costs

No further costs have been identified for this module.

You do not need to pass all assessment components to pass the module.

Students can register for this module without taking any assessment.

##### Assessment group D2
Weighting Study time
CS137 Coursework 10%
CS137 Coursework 10% 10 hours
On-campus Examination 80% 10 hours

CS137 exam

~Platforms - AEP

• Answerbook Pink (12 page)
##### Assessment group R1
Weighting Study time
Online Examination 100%

CS137 resit exam

~Platforms - AEP

• Online examination: No Answerbook required
##### Feedback on assessment

Marked scripts available on students' request

## Courses

This module is Core for:

• Year 1 of UCSA-G4G1 Undergraduate Discrete Mathematics
• Year 1 of UCSA-G4G3 Undergraduate Discrete Mathematics

This module is Option list B for:

• Year 1 of UMAA-G100 Undergraduate Mathematics (BSc)
• Year 1 of UMAA-G103 Undergraduate Mathematics (MMath)
• Year 1 of UMAA-G106 Undergraduate Mathematics (MMath) with Study in Europe
• Year 1 of UMAA-G1NC Undergraduate Mathematics and Business Studies
• Year 1 of UMAA-G1N2 Undergraduate Mathematics and Business Studies (with Intercalated Year)
• Year 1 of UMAA-GL11 Undergraduate Mathematics and Economics
• Year 1 of UECA-GL12 Undergraduate Mathematics and Economics (with Intercalated Year)
• Year 1 of UMAA-GV17 Undergraduate Mathematics and Philosophy
• Year 1 of UMAA-GV18 Undergraduate Mathematics and Philosophy with Intercalated Year
• Year 1 of UMAA-G101 Undergraduate Mathematics with Intercalated Year