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Module MAU23302: Euclidean and NonEuclidean Geometry
 Credit weighting (ECTS)

5 credits
 Semester/term taught

Michaelmas term 201920
 Contact Hours

11 weeks, 3 lectures per week

 Lecturer
 Prof. David Wilkins
 Learning Outcomes
 On successful completion of this module, students will be able to:
 justify with reasoned logical argument basic properties
of triangles, circles and polygons in the Euclidean plane;
 describe measures of curvature, both extrinsic and
intrinsic, applicable to smooth surfaces in threedimensional
Euclidean space;
 identify, and justify with reasoned logical argument,
significant geometric features and properties of the
hyperbolic plane, and the corresponding features
and properties of the disk that represent them in the
Poincaré disk model of the hyperbolic plane.
 Module Content
 Aims to introduce complex variable theory and reach the residue theorem,
applications of that to integral evaluation.
 Euclidean geometry: an exploration of Euclid's
Elements of Geometry, based on editions
freely available online, with detailed discussion of the
definitions, axioms and propositions of Book 1, followed
by discussion of a selection of significant results
contained in Books 2—6.
 Curvature of surfaces: a discussion of some of the
principal results of C.F. Gauss's General
Investigations of Curved Surfaces.
 The hyperbolic plane: the Poincaré disk model
of the hyperbolic plane, geodesics and curvature,
homogeneity, the representation of isometries
as Möbius transformations.
 Module Prerequisite
 None
 Assessment Detail

This module will be examined in a 2 hour examination in Trinity term.
Supplementals if required will consist of 100% exam.