# MAS1701 : Logic, Sets and Counting

• Offered for Year: 2020/21
• Module Leader(s): Dr Alina Vdovina
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 1 Credit Value: 10 ECTS Credits: 5

#### 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

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture14:504:50Synchronous On-Line Material
Structured Guided LearningLecture materials181:0018:00Non-Synchronous Activities
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of In Course Assessment
Scheduled Learning And Teaching ActivitiesWorkshops14:504:50Present in Person
Structured Guided LearningStructured non-synchronous discussion91:009:00Non Synchronous Discussion to Support Learning
Scheduled Learning And Teaching ActivitiesDrop-in/surgery21:002:00Office Hour or Discussion Board Activity
Guided Independent StudyIndependent study146:2046:20Preparation time for lectures, background reading, coursework review
Total100:00
##### Teaching Rationale And Relationship

Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.
Alternatives will be offered to students unable to be present-in-person due to the prevailing C-19 circumstances.
Student’s should consult their individual timetable for up-to-date delivery information.

#### Assessment Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

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

##### Other Assessment
Description Semester When Set Percentage Comment
Written exercise1M20N/A
Written exercise1M20N/A
Written exercise1M60Alternative assessment
##### Assessment Rationale And Relationship

The course assessments 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.