Topic outline
Essential Information
The Wednesday, 11:00-13:00 lectures are held:
- In person, at the Maths Lecture Theatre (MLT, Maths Building).
- Online on MS Teams, at the following link: https://teams.microsoft.com/l/meetup-join/19%3ameeting_NmM4Mjk4YjAtNTIwMC00ZmQxLWE4ZGItYzNkOGEzMDU2YjJh%40thread.v2/0?context=%7b%22Tid%22%3a%22569df091-b013-40e3-86ee-bd9cb9e25814%22%2c%22Oid%22%3a%221bfee6cc-5f99-4957-ad66-c5f363b293d5%22%7d
The Thursday, 14:00-16:00 lectures are held:
- In person, at the Peston Lecture Theatre (G.10, Graduate Centre).
- Online on MS Teams, at the following link: https://teams.microsoft.com/l/meetup-join/19%3ameeting_NGQ4Y2Y2MDQtMGMyMy00NDFhLTg0MzAtNTJhZWNkZDVkZmYz%40thread.v2/0?context=%7b%22Tid%22%3a%22569df091-b013-40e3-86ee-bd9cb9e25814%22%2c%22Oid%22%3a%221bfee6cc-5f99-4957-ad66-c5f363b293d5%22%7d
The typeset lecture notes can be found in the Lecture Material tab below, in the Notes section.
Pre-recorded lectures from 2020/21, which cover the same material, can be found in the Lecture Material tab below, in the Pre-recorded Lectures section.
Office hours will be held immediately after each lecture (roughly, Wednesday 13:15-13:45 and Thursday 16:15-16:45).
- Those attending in person can come to my office after the lecture.
- Those attending online should remain in the MS Teams meeting until I rejoin.
The coursework deadlines are set on the following dates and times:
- Coursework Submission 1 (Week 3): 23:59, Wednesday, 9 February
- Coursework Submission 2 (Week 5): 23:59, Wednesday, 23 February
- Coursework Submission 3 (Week 8): 23:59, Wednesday, 16 March
- Coursework Submission 4 (Week 10): 23:59, Wednesday, 30 March
- Coursework Submission 5 (Week 12): 23:59, Wednesday, 13 April
There are extra Office Hours a few days before the final exam:
- 13:00-14:00, Tuesday, 24 May: Online office hours—MS Teams, https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZDcyZmQ1NTgtMDIxZi00OTFiLWEyMDAtMTBmZWYxMDRhZGNm%40thread.v2/0?context=%7b%22Tid%22%3a%22569df091-b013-40e3-86ee-bd9cb9e25814%22%2c%22Oid%22%3a%221bfee6cc-5f99-4957-ad66-c5f363b293d5%22%7d
- 14:00-15:00, Tuesday, 24 May: In-person office hours (Room MB-513, Maths Building)
Problem Sheets
There is one problem sheet released every week, covering the material from that week. One question from each problem sheet (except for the last sheet) will be used as half of a coursework submission.
All the problem sheets for the module can be found below.
Coursework Submissions
There are 5 coursework submissions for this module, with each worth 4% of the total module mark.
The coursework submission portals can be found below.
Final exam
The final exam will be held online in mid-May and will be worth 80% of the total module mark.
The general format of the final exam will be the same as in the previous semester:
- The exam will be contained within a QMPlus quiz and will be available for a period of 24 hours. Upon accessing the exam, you will then have a 3-hour window to submit your solutions. Moreover, all submissions will close at the end of the 24-hour period.
- This will be a handwritten exam—you will be asked to submit your handwritten solutions as a single PDF file.
- You will be expected to show your working and your reasoning for all your solutions. I am more interested in how well you understand the steps, rather than whether you get the correct number in the end.
- The format of the exam (i.e. what is examinable, types of questions) will be similar to the the previous year's MTH5113 exam.
Regarding what is allowed and what is an academic offence:
- The exam is open-book—you can use your notes, books, and the Internet as sources.
- You may not work or communicate with others on the exam.
- You may not use the Internet to ask for a solution to an exam question, or to copy down any solution you find to an exam question.
See the link below for MTH5113 exams from previous years. Further information (previous solutions, additional resources) will be added here after the end of term.
Syllabus
The module will cover the following general topics:
- Vector algebra and calculus
- Tangent vectors, calculus of vector-valued functions
- The geometry of curves
- Parametrisations, tangent lines, orientation, curve integrals
- The geometry of surfaces
- Parametrisations, tangent planes, orientation, surface integrals
- Applications
- Constrained optimisation and Lagrange multipliers; Green's, Stokes', and divergence theorems
- Vector algebra and calculus
Learning outcomes
At the end of this module, students should be able to:
- Precisely define and describe basic geometric concepts, such as curves and surfaces.
- Explain how geometric properties of curves and surfaces and be captured and quantified, and apply apply this knowledge in order to perform computations.
- Demonstrate how ideas from differential and integral calculus can be extended to geometric settings.
- Demonstrate how calculus and linear algebra can be connected to and applied to geometric concepts and questions.
- Explain the main ideas behind proofs of basic results in curve and surface geometry.
- Explain some ways that geometric ideas can be applied to questions in other areas of mathematics or outside of mathematics.
Notes
Pre-Recorded Lectures (2020/21)
Below are the pre-recorded lectures from the 2020/21 iteration of MTH5113, which was taught fully online.
Week 1
Content covered: Sections 2.1, 2.2, 2.3, 2.4 of Lecture Notes.
Week 2
Content covered: Sections 2.5, 2.6, 2.7, 2.8 of Lecture Notes.
Week 3
Week 4
Week 5
Content covered: Sections 3.6, 3.7, 3.8, 3.9 of Lecture Notes.
Week 6
Content covered: Sections 3.10, 4.1, 4.2 of Lecture Notes.
Week 7
No lectures this week.
Week 8
Content covered: Sections 4.3, 4.4, 4.5 of Lecture Notes.
Week 9
Content covered: Sections 4.6, 4.7, 4.8 of Lecture Notes.
Week 10
Content covered: Sections 4.9, 4.10, 5.1 of Lecture Notes.
Week 11
Content covered: Sections 5.2, 5.3, 5.4 of Lecture Notes.
Week 12
Content covered: Sections 5.5, 5.6, 5.7, 5.8 of Lecture Notes.
Additional Reading
Graphical Tools
Assessments and Marks
The assessments for this module will consist of:
- Five courseworks, each counting for 4% of your module mark. There will be a new coursework every two weeks.
- The final exam in May, which will count for 80% of your module mark.
See the Assessments tab for more information.