2016/17 Undergraduate Module Catalogue

COMP1421 Fundamental Mathematical Concepts

10 creditsClass Size: 165

Module manager: Dr Isolde Adler
Email: l.m.adler@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2016/17

This module is not approved as a discovery module

Module summary

This module focuses on some mathematical concepts and techniques that are fundamental to computing. One of the primary aims is to teach students how to understand and how to construct correct mathematical arguments, so the module begins with an introduction to logic. We study propositions and how they combine using logical operators and quantifiers (concepts which underpin automated reasoning and system specification). This leads to a study of rules of inference and different proof techniques -- direct methods, proof by contradiction and mathematical induction -- which can be used for, among many things, verification of program correctness, system security, complexity analysis. These concepts are then applied in the formal introduction and study of sets (fundamental discrete structure that all other discrete structures are built on), functions (e.g. for analysis of computational complexity), relations (the basis of relational databases), vectors and matrices (fundamental for applications in mathematics, computer science, physics and engineering), and their properties.

Objectives

On completion of this module, students should be able to: understand and be proficient in applying some of the mathematical concepts and techniques that are fundamental to computing, and in particular those that fall within the areas of logic, set theory, functions and relations, vectors and matrices.

Learning outcomes
On completion of the year/programme students should have provided evidence of being able to:
- demonstrate a familiarity with the basic concepts, information, practical competencies and techniques which are standard features of the discipline;
- be able to interpret and evaluate the underlying concepts and principles of the discipline;
- evaluate qualitative and/or quantitative data;
- demonstrate an ability to evaluate the appropriateness of different approaches to problem solving associated with the discipline;
- appreciate their strengths and weaknesses as learners;
- demonstrate computational thinking including its relevance to everyday life;
- operate computing equipment effectively, taking into account its logical and physical properties.

Syllabus

Propositional logic: propositions, connectives, truth tables, tautologies, contradictions; predicates, quantifiers; proof techniques (including mathematical induction). Set theory: sets, set operations, Venn diagrams, set equality, subsets, cardinality. Relations: relations on a set, inverse relations, equivalence relations, orders. Functions: domain and range, inverse functions, composition of functions, properties of functions. Vectors and matrices (addition and multiplication, distributive and associative laws, non-commutativity, identity matrix and inverse of square matrices.

Teaching methods

Delivery type	Number	Length hours	Student hours
Class tests, exams and assessment	1	2.00	2.00
Lecture	22	1.00	22.00
Tutorial	10	1.00	10.00
Private study hours			66.00
Total Contact hours			34.00
Total hours (100hr per 10 credits)			100.00

Private study

Taught session preparation: 18 hours
Taught session follow-up: 18 hours
Self-directed study: 7 hours
Assessment activities: 23 hours

Opportunities for Formative Feedback

Attendance and formative assessment

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
Problem Sheet	Problem Sheet	5.00
Problem Sheet	Problem Sheet	5.00
Problem Sheet	Problem Sheet	5.00
Problem Sheet	Problem Sheet	5.00
Total percentage (Assessment Coursework)		20.00

This module is re-assessed by exam only.

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 00 mins	80.00
Total percentage (Assessment Exams)		80.00

This module is re-assessed by exam only.

Reading list

The reading list is available from the Library website

Last updated: 07/09/2016

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