Undergraduate Course: Geometry (MATH10074)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Course type  Standard 
Availability  Available to all students 
Credit level (Normal year taken)  SCQF Level 10 (Year 3 Undergraduate) 
Credits  10 
Home subject area  Mathematics 
Other subject area  None 
Course website 
None 
Taught in Gaelic?  No 
Course description  This course is an introduction to differential geometry, which is the study of geometry using methods of calculus and linear algebra. The course begins with curves in euclidean space; these have no intrinsic geometry and are fully determined by the way they bend and twist (curvature and torsion).
The rest of the course will then develop the theory of surfaces. This will be done in the modern language of differential forms. Surfaces possess a notion of intrinsic geometry and many of the more advanced aspects of differential geometry can be demonstrated in this simpler context. The culmination of the course will be a sketch proof of the GaussBonnet theorem, a remarkable connection between the curvature of surfaces and their topology. 
Information for Visiting Students
Prerequisites  None 
Displayed in Visiting Students Prospectus?  No 
Course Delivery Information

Delivery period: 2013/14 Semester 2, Available to all students (SV1)

Learn enabled: Yes 
Quota: None 
Web Timetable 
Web Timetable 
Course Start Date 
14/01/2014 
Breakdown of Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )

Additional Notes 

Breakdown of Assessment Methods (Further Info) 
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %

Exam Information 
Exam Diet 
Paper Name 
Hours:Minutes 


Main Exam Diet S2 (April/May)  MATH10074 Geometry  2:00   
Summary of Intended Learning Outcomes
1. An ability to compute the FrenetSerret frame of space curves and determine their torsion and curvature.
2. An ability to perform simple manipulations with differential forms.
3. An understanding of the first and second fundamental forms of a surface and its principal curvatures. An ability to compute simple examples.
4. An ability to calculate geodesics on surfaces in simple examples.
5. An ability to apply Stokes' Theorem to simple examples.
6. An ability to apply the GaussBonnet theorem to simple examples. 
Assessment Information
See 'Breakdown of Assessment Methods' and 'Additional Notes' above.

Special Arrangements
None 
Additional Information
Academic description 
Not entered 
Syllabus 
Curves in Euclidean space, regularity, velocity, arclength, FrenetSerret frame, curvature and torsion, equivalence problem.
Tangent vectors, vector fields, differential forms, Poincare¿s Lemma, moving frames, connection forms, structure equations.
Surfaces, first and second fundamental forms, curvature, isometry, Theorema Egregium, geodesics on surfaces, integration of forms, statement of general Stokes' theorem, Euler characteristic, GaussBonnet theorem (sketch proof). 
Transferable skills 
Not entered 
Reading list 
Not entered 
Study Abroad 
Not Applicable. 
Study Pattern 
See 'Breakdown of Learning and Teaching activities' above. 
Keywords  Geom 
Contacts
Course organiser  Dr James Lucietti
Tel: (0131 6)51 7179
Email: J.Lucietti@ed.ac.uk 
Course secretary  Mrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk 

