GEOMETRY OF PLANE CURVES

The objective of the course is to gain a basic understanding of plane curves, the starting point for more general geometry . The initial emphasis is on algebraic curves, and latterly on differentiable curves. All the material is covered in detail in my books "Elementary Geometry of Algebraic Curves" and "Elementary Geometry of Differentiable Curves". The course will comprise a selection (to be determined as the course proceeds) of the following broad topics :-

Lines, circles and general conics: general ground fields: affine planes: algebraic curves and their zero sets: review of polynomials: affine equivalence: affine conic types: singular points: tangents: rationality: projective planes: curves, singularities, equivalence and tangents in the projective plane: flexes and their configurations on cubics: intersections and Bezout's Theorem: cubics over the complex field: linear systems: group structure on the cubic: the Euclidean plane: parametrized curves: tangents and normals: curvature: Existence and Uniqueness Theorem: contact with lines: inflexions and cusps: contact with circles: vertices: evolutes: Four Vertex Theorem.