Global Opportunities

MAS1701 : Logic, Sets and Counting

Semesters
Semester 1 Credit Value: 10
ECTS Credits: 5.0

Aims

To present the notion and techniques of proof, illustrated by results in set theory and basic combinatorics. To stimulate logical thinking and to develop students' skills at constructing mathematical arguments.

Module summary

This module introduces the concept of proof in mathematics. Proof sets mathematics apart from other subjects: within mathematics we can prove statements are unambiguously true, rather than simply collecting evidence in support of statements as in other areas of science. The objects studied in this module are sets and functions between sets. Important techniques of proof presented will include proof by induction and proof by contradiction. The module will conclude with a variety of methods for counting the number of elements in sets.

Outline Of Syllabus

Logic and techniques of proof. Argument by contradiction and mathematical induction.

Sets and set operations.

Functions: composition of functions; injective and surjective functions.

Counting arguments for the number of elements in a set: sequences, permutations and combinations.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes – Synchronous On-Line
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of In Course Assessment
Scheduled Learning And Teaching ActivitiesDrop-in/surgery51:005:00Synchronous On-Line
Guided Independent StudyIndependent study153:0053:00Preparation time for lectures, background reading, coursework review
Total100:00
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
PC Examination1201A80N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10Coursework assignment
Prob solv exercises1M10Coursework assignment
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.

Reading Lists

Timetable