CS13015 Sets and Proofs
Introductory description
This module introduces some of the fundamental mathematical ideas
that are used in the design and analysis of computer systems and software.
The module makes you familiar with basic concepts and notation, helps you
to develop a good understanding of mathematical proofs, and enables you
to apply mathematics to solving computer science problems. The focus in
CS130 is on discrete (i.e. not continuous) mathematics.
Module aims
The module aims to provide students with sufficient mathematical knowledge to enable them to understand the foundations of their subject for both study purposes and later career development.
It seeks to bridge the gap in style and content between Alevel and university mathematics, and to introduce students to the language and methods of professional mathematics.
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.
 The axiomatic method. Basic concepts, axioms, definitions, theorems. Finite and infinite sets. Natural numbers, induction.
 Logic. Statements, truth values, Boolean operators, laws of propositional logic. Predicates, quantifiers, laws of predicate logic.
 Sets. Connection between sets and predicates. Operations on sets. Laws of set operations.
 Relations. Relation composition and inverse. Properties of relations. Equivalence relations, equivalence classes, quotient sets. Partial orders..
 Functions. Properties of functions. Equinumerous sets. Countable and uncountable sets.
 Graphs. Graph isomorphism. Graph connectivity. Eulerian and Hamiltonian graphs.
 Mathematical induction.
Learning outcomes
By the end of the module, students should be able to:
 Understand and use basic mathematical terminology.
  Understand the role of formal definitions and proofs and be able to apply them in problem solving.
  Understand the basics of propositional and predicate logic.
  Understand the basics of elementary set theory.
  Understand the basics of mathematical relations and functions.
  Understand the basics of graph theory.
Indicative reading list
Please see Talis Aspire link for most up to date list.
View reading list on Talis Aspire
Subject specific skills
Problem Solving
Understanding Abstract Concepts
Transferable skills
Critical Thinking
Creativity
Study time
Type  Required 

Lectures  30 sessions of 1 hour (20%) 
Seminars  9 sessions of 1 hour (6%) 
Private study  111 hours (74%) 
Total  150 hours 
Private study description
Background study
Problems solving
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 D4
Weighting  Study time  

Problem Set 0  1%  
Formative problem sheet (mock) for flat credit. This assessment is eligible for selfcertification (waive). 

Problem Set 1  3%  
Summative problem sheet for flat credit (1% for submission, 2% for submission of peer feedback). This assessment is eligible for selfcertification (waive). 

Problem Set 2  3%  
Summative problem sheet for flat credit (1% for submission, 2% for submission of peer feedback). This assessment is eligible for selfcertification (waive). 

Problem Set 3  3%  
Summative problem sheet for flat credit (1% for submission, 2% for submission of peer feedback). This assessment is eligible for selfcertification (waive). 

Problem Set 4  10%  
Summative problem sheet. This assessment is eligible for selfcertification (extension). 

Inperson Examination  80%  
CS130 exam

Assessment group R3
Weighting  Study time  

Inperson Examination  Resit  100%  
CS130 resit exam

Feedback on assessment
There will be 3 formative small problem sheets, and feedback on problem sheets will be given in seminar sessions.
Courses
Course availability information is based on the current academic year, so it may change.This module is Core for:

UCSAG500 Undergraduate Computer Science
 Year 1 of G500 Computer Science
 Year 1 of G500 Computer Science

UCSAG503 Undergraduate Computer Science MEng
 Year 1 of G500 Computer Science
 Year 1 of G503 Computer Science MEng
 Year 1 of G503 Computer Science MEng
 Year 1 of UCSAI1N1 Undergraduate Computer Science with Business Studies
This module is Optional for:
 Year 1 of UCSAG406 Undergraduate Computer Systems Engineering
 Year 1 of UCSAG408 Undergraduate Computer Systems Engineering