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: | 5.0 |
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
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 Activities | Lecture | 1 | 4:50 | 4:50 | Synchronous On-Line Material |
| Structured Guided Learning | Lecture materials | 18 | 1:00 | 18:00 | Non-Synchronous Activities |
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of In Course Assessment |
| Scheduled Learning And Teaching Activities | Workshops | 1 | 4:50 | 4:50 | Present in Person |
| Structured Guided Learning | Structured non-synchronous discussion | 9 | 1:00 | 9:00 | Non Synchronous Discussion to Support Learning |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 2 | 1:00 | 2:00 | Office Hour or Discussion Board Activity |
| Guided Independent Study | Independent study | 1 | 46:20 | 46:20 | Preparation time for lectures, background reading, coursework review |
| Total | 100:00 |
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 exercise | 1 | M | 20 | N/A |
| Written exercise | 1 | M | 20 | N/A |
| Written exercise | 1 | M | 60 | Alternative 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.
Reading Lists
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS1701's Timetable