Synopsis for Geometry

Overview

These lectures give an introduction to elementary ideas in the geometry of euclidean space through vectors.

Learning Outcomes

By the end of the course students will have a detailed knowledge of euclidean geometry in two and three dimensions.

Synopsis

Euclidean geometry in two and three dimensions approached by vectors and coordinates. Vector addition and scalar multiplication. The scalar product, equations of planes, lines and circles.

The vector product in three dimensions. Scalar triple products and vector triple products, vector algebra.

Rotations, reflections, isometries.

Parametric representation of curves, tangents; conics (normal form only), focus and directrix. Simple surfaces: spheres, right circular cones.

1. J. Roe, Elementary Geometry (Oxford Science Publications, 1992), Chapters 1, 2.2, 3.4, 4, 7.1, 7.2, 8.1–8.3.

Alternative Reading

1. M. Reid and B. Szendroi, Geometry and Topology (Cambridge University Press, 2005), Chapter 1.
2. D. A. Brannan, M. F. Esplen and J. J. Gray, Geometry (Cambridge University Press, 1999), Chapter 1.
3. P. M. Cohn, Solid Geometry (Routledge and Kegan Paul, 1961), Chapters 1–3.
4. R. Fenn, Geometry (Springer, 2001), Chapters 2, 5, 7.
5. J. E. Marsden and A. J. Tromka, Vector Calculus (McGraw-Hill, fourth edition, 1996), Chapters 1, 2.
6. J. Silvester, Geometry, Ancient and Modern (Oxford University Press, 2001), Chapters 3, 5, 6, 7.