Introduction to Geometry2020/2021
MATH20222

Lecturers: Simon Peacock and Ben Smith

Course Videos: Available on Blackboard

Synchronous sessions held via Zoom:
Link available via Blackboard

• Review Session: Monday 2pm-3pm
• Tutorial: Friday 10am-11am.
• Office hours: Thursday 1:30pm-2:30pm

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Outline of course

• Euclidean Geometry
• Differential Geomtry
• Conic sections
• Projective Space

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Lecture notes

Week 1: Introduction to Euclidean geometry

Week 2: Linear operators and orientation

Week 3: Orthogonal operators and Euler's rotation theorem

Week 4: Determinant, area and volume

Homework

Exercise Sheet 1. (Solutions)

Exercise Sheet 2. (Solutions)

Exercise Sheet 3.

Exercise Sheet 4.

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Recommended reading

None of these books are required for the course, but could be helpful to supplement the lectures and notes if you get confused.

• Brannan, David Geometry, Cambridge University Press

• Dubrovin; Fomenko; and Novikov Modern geometry- methods and applications. Part I, Springer

• Morita, Shigeyuki Geometry of differential forms, AMS

• O'Neill, Barrett Elementary differential geometry, Academic Press

• Pressley, Andrew Elementary differential geometry, Springer