Module Information

Module Identifier
CS10310
Module Title
INTRODUCTION TO THEORETICAL COMPUTER SCIENCE
2010/2011
Co-ordinator
Semester
Semester 1
Mutually Exclusive
Pre-Requisite
A level or AS level maths.

Course Delivery

Delivery Type Delivery length / details
Lecture Up to 22 hours

Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   Written exam  80%
Semester Assessment assignment (approx 10 hours)  20%
Supplementary Exam 2 Hours   Resit failed examination and/or resubmission of failed/non-submitted coursework components or ones of equivalent value.  100%

Learning Outcomes

On successful completion of this module students should be able to:

state basic definitions and results of the theory of computing;

provide formal definitions of programming language constructs

relate theory to the elements of a modern programming language

recognize that there are different categories of problems in computing.

Brief description

This module introduces basic concepts and results of theoretical computer science. It is intended for students with a background in computing who wish to deepen their understanding of programming concepts and the theoretical underpinning of computer science.

Content

1. Sets, functions and relations - 3 Lectures

Motivation - relationship with programs. What are sets and how do we describe them. When to use enumeration and when to use predicates. The set of truth values. Cardinality. Subsets. Using sets to specify pre- and post-conditions for programs. Sets and sequences. Set union, intersection, difference. Universal set. Complement of a set. Venn-Euler diagrams. Cartesian product. Powerset. Examples of proofs.

2. Languages and Problems - 13 Lectures

Motivation: computation entails using language to describe and solve problems.
Symbols, alphabets. Strings. String concatenation. Alphabets and strings.
Languages. Language union, intersection, difference and symmetric difference. Language concatenation. Kleene star.
Regular expressions and regular languages. Deterministic finite automata. Nondeterministic Finite Automata. Languages that are not regular. The Pumping Lemma (simple and general forms). Proving that a language is/is not regular. Closure properties of regular language. Using the closure properties to prove that a language is not regular.
Context free languages. Context free grammars. Derivations of context free grammars. Context free grammars and regular grammars. Pushdown automata. Languages that are not context free. Context free languages are not closed under intersection. Context free languages are not closed under complementation. Context free languages are closed under union.

3. Advanced Topics - 4 Lectures

What are Turing machines? Beyond context free languages. Example. What does Computable mean? The Halting Problem.

Module Skills

Skills Type Skills details
Application of Number Inherent to subject. Assessed in assignment and exam
Communication no
Improving own Learning and Performance Reflection and self-learning will be encouraged during all sessions. In addition the assignment will allow students to reflect on their learning to date.
Information Technology In practicals students will relate concepts to computing languages
Personal Development and Career planning no
Problem solving Inherent to subject. Assessed in assignment and exam.
Research skills no
Subject Specific Skills See contents
Team work no