# Logical Foundations

## Course summary

Course code: MATH1110
Level: 4
Credits: 15
School: Architecture, Computing and Hums
Department: Mathematical Sciences
Course Coordinator(s): Yvonne Fryer

## Specification

### Aims

This course contains the logic and mathematical ideas needed to underpin a rigorous approach to computing. The emphasis will be on developing precise thinking, looking at modelling data and processes, introducing some reasoning techniques and investigating the use of statistics.

### Learning outcomes

At the end of the course the student should be able to:
A. Develop a facility with algebraic expressions, number types and their manipulation.
B. Understand the nature of sets and their use in computing.
C. Use logic to reason about statements and apply to practical applications.
D. Use simple statistics for data interpretation.

### Indicative content

Review and revision of basic algebra:
Extracting relationships from data, manipulation, solving simple equations, rearranging formulae.

Number:
Number types and their representation in computing. Number bases, binary and hexadecimal, and arithmetic operations in these bases.

Sets:
Definitions, laws of operation, Venn diagrams, product set and projection mappings.

Propositional logic:
Translation between natural language and logic, truth tables, laws of propositional calculus.
Validity of arguments, Boolean algebra and application to circuits.

Predicate logic:
Predicate Logic as Generalised Propositional Logic, Scope of quantifiers, N-place predicates.
Application of logic in programming.

Statistics:
Interpreting results, discrete and continuous distributions, measures of average and range, graphical presentation.

Formal Languages:
The structure of formal languages, Syntax, Semantics.

### Teaching and learning activity

Concepts will be introduced in lectures and problem solving will be done through tutorials.
Student time will be: Lecture 67% and Tutorial 33%.

Learning Time (1 credit = 10 hours)

Scheduled contact hours:

Note: include in scheduled time: project supervision, demonstrations, practical classes and workshops, supervised time in studio or workshop, scheduled lab work , fieldwork, external visits, work-based learning where integrated into a structured academic programme:
lectures 24
seminars
supervised practical sessions
tutorials 12

other scheduled time
Guided independent study

Note: include in guided independent study preparation for scheduled sessions, follow up work, wider reading or practice, revision:
Independent coursework 25
Independent laboratory work
other non-scheduled time 89
Placements (including work placement and year abroad)
Total hours (’Should be equal to credit x 10’) 150

### Assessment

Assignment - 50%
Students submit work at intervals through the course that is marked and returned providing feedback.

Exam - 50%
The exam is 2 hours at the end of the course.

Pass mark 40%.