Logical Foundations

Module summary

Module code: MATH1110
Level: 4
Credits: 15
School: Liberal Arts and Sciences
Department: Computing and Mathematical Sci.
Module 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, modelling data and processes and introducing reasoning techniques.

Learning outcomes

Learning Outcomes: on successful completion of this course a student will be able to:
1 Demonstrate an understanding of sets and propositional logic and their application in computing.
2 Apply arithmetic and algebraic expressions in a range of number types and bases.
3 Demonstrate an understanding and application of formal languages and predicate logic.

Indicative content

Basic arithmetic and algebra.
Extracting relationships from data, manipulation, solving simple equations, rearranging formulae.
Function definitions and types, function composition and inversion. Logarithmic, exponential and trigonometric functions.
Number types and their representation in computing.
Number bases, binary and hexadecimal, and arithmetic operations in these bases.
Complex numbers; Definition of i, Argand diagram, manipulation of complex numbers.
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 as Generalised Propositional Logic, Scope of quantifiers, N-place predicates.
Application of logic in programming.
The structure of formal languages, Syntax, Semantics.