MAS8713 : Curves and Surfaces
MAS8713 : Curves and Surfaces
- Offered for Year: 2024/25
- Module Leader(s): Dr Stuart Hall
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
Your programme is made up of credits, the total differs on programme to programme.
Semester 2 Credit Value: | 10 |
ECTS Credits: | 5.0 |
European Credit Transfer System | |
Pre-requisite
Modules you must have done previously to study this module
Code | Title |
---|---|
MAS2804 | |
MAS2707 |
Pre Requisite Comment
N/A
Co-Requisite
Modules you need to take at the same time
Co Requisite Comment
N/A
Aims
To give students a grounding in the theory of curves and surfaces in 3 dimensions. Students will learn about parameterised curves and the use of local surface patches to describe surfaces. Students will learn about the precise definition of curvature and compute this for many famous examples. Students will see applications to the isoperimetric inequality and minimal surfaces (soap bubbles).
Module Summary
The theory of geometry in the three dimensional space is important to mathematicians as it is the theory of the world as we find it. It has been studied since time out of mind and continues to this day as an active area of research. This module focuses on the mathematical description of the shape of curves and surfaces. With these notions in hand, we can describe many interesting phenomena such as why folding a pizza slice is the best way of eating it or why soap bubbles take the shape that they do. In the early years of the 20th century, these ideas became the cornerstone for the mathematics that underpinned general relativity, variational methods, Lagrangian dynamics and geometry in higher dimensions. This module will focus on computing examples so would suit a student that likes to apply results to specific cases.
Outline Of Syllabus
Parameterised curves: examples, arc length, curvature torsion and the Frenet--Serret formulae. The isoperimetric problem. Parameterising surfaces: examples, tangents to surfaces. The Ist fundamental form and isometries. The IInd fundamental form and curvature. Selected topics: minimal surfaces and soap bubbles, Weierstrass parameterisation of minimal surfaces.
Learning Outcomes
Intended Knowledge Outcomes
Students will be able to precisely define the notions of curve, surface and related geometric concepts such as the curvature. They will be able to give examples of curves and surfaces and compute the geometric notions for these examples. They will learn how certain special curves and surfaces arise as the critical points of variational problems.
Intended Skill Outcomes
Students will be able to compute curvature and torsion of a parameterised curve and the $I^{st}$ and $II^{nd}$ fundamental forms of a parameterised surface.
Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.
Teaching Methods
Teaching Activities
Category | Activity | Number | Length | Student Hours | Comment |
---|---|---|---|---|---|
Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in course assessments |
Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes |
Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
Guided Independent Study | Independent study | 58 | 1:00 | 58:00 | Preparation time for lectures, background reading, coursework review |
Total | 100:00 |
Jointly Taught With
Code | Title |
---|---|
MAS3713 | Curves and Surfaces |
Teaching Rationale And Relationship
The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.
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.
Reading Lists
Assessment Methods
The format of resits will be determined by the Board of Examiners
Exams
Description | Length | Semester | When Set | Percentage | Comment |
---|---|---|---|---|---|
Written Examination | 120 | 2 | A | 80 | N/A |
Exam Pairings
Module Code | Module Title | Semester | Comment |
---|---|---|---|
Curves and Surfaces | 2 | N/A |
Other Assessment
Description | Semester | When Set | Percentage | Comment |
---|---|---|---|---|
Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.
Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.
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.
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS8713's Timetable
Past Exam Papers
- Exam Papers Online : www.ncl.ac.uk/exam.papers/
- MAS8713's past Exam Papers
General Notes
N/A
Welcome to Newcastle University Module Catalogue
This is where you will be able to find all key information about modules on your programme of study. It will help you make an informed decision on the options available to you within your programme.
You may have some queries about the modules available to you. Your school office will be able to signpost you to someone who will support you with any queries.
Disclaimer
The information contained within the Module Catalogue relates to the 2024 academic year.
In accordance with University Terms and Conditions, the University makes all reasonable efforts to deliver the modules as described.
Modules may be amended on an annual basis to take account of changing staff expertise, developments in the discipline, the requirements of external bodies and partners, and student feedback. Module information for the 2025/26 entry will be published here in early-April 2025. Queries about information in the Module Catalogue should in the first instance be addressed to your School Office.