Unit information: Introduction to Geometry in 2021/22

Unit name Introduction to Geometry MATH20004 20 I/5 Teaching Block 2 (weeks 13 - 24) Dr. Hassannezhad Not open MATH11005 Linear Algebra and Geometry, MATH10012 ODEs, Curves and Dynamics, and MATH10011 Analysis None School of Mathematics Faculty of Science

Description including Unit Aims

Unit Aims

The aim of this unit is to introduce fundamental concepts in geometry in a hands-on and rigorous way, focused on curves and surfaces, and to lay the foundations for more advanced courses in later years.

Unit Description

Geometry is central to mathematics, both as a subject in its own right and as an essential viewpoint on nearly every area of pure and applied mathematics. This course focuses on the geometry of curves and surfaces in R2 and R3, continuing on from calculus.

A key concept is the curvature of a surface, which describes locally how it bends, whether it is flat like Euclidean space, positively curved like a sphere, or, less-familiarly, negatively curved like a saddle. A major goal is to prove the Gauss-Bonnet theorem, which links the curvature of a surface to its overall shape.

Relation to Other Units

The unit complements MATH20901 Multivariable Calculus and MATH20006 Metric Spaces and leads into later units in geometry such as MATHM0037 Geometry of Manifolds, MATH30018 Fields, Forms & Flows and MATH30001 Topics in Modern Geometry.

Intended Learning Outcomes

By the end of the course the students should

• have developed an understanding of basic notions and results in differential geometry, like tangents, normals, curvature and Gauss-Bonnet
• know and be able to use basic properties of Euclidean, spherical and hyperbolic geometries
• understand, be able to prove and apply the methods in the course to the description and solution of problems from pure and applied mathematics.

Teaching Information

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

Assessment Information

90% Timed, open-book examination 10% Coursework

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH20004).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.