# CS130-15 Mathematics for Computer Scientists 1

Department
Computer Science
Level
Dmitry Chistikov
Credit value
15
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry

##### 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 and probability.

##### 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 A-level 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
• Basic probability
##### 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.

##### 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

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 D3
Weighting Study time
Problem Set 0 1%

Formative problem sheet (mock) for flat credit

Problem Set 1 3%

Summative problem sheet for flat credit (1% for submission, 2% for submission of peer feedback)

Problem Set 2 3%

Summative problem sheet for flat credit (1% for submission, 2% for submission of peer feedback)

Problem Set 3 3%

Summative problem sheet for flat credit (1% for submission, 2% for submission of peer feedback)

Problem Set 4 10%

Summative problem sheet

In-person Examination 80%

CS130 exam

##### Assessment group R2
Weighting Study time
In-person 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

This module is Core for: