Module MATH4161: ALGEBRAIC TOPOLOGY IV

Department: Mathematical Sciences

MATH4161: ALGEBRAIC TOPOLOGY IV

Prerequisites

• Mathematics modules to the value of 100 credits in Years 2 and 3, with at least 40 credits at Level 3 and including Topology III (MATH3281).

Corequisites

• None.

Excluded Combination of Modules

• None.

Aims

• Provide a deeper knowledge in the field of topology (a balanced introduction having been provided in Topology III (MATH3281)).

Content

• Homotopy theory of cell complexes.
• Fundamental group.
• Covering spaces.
• Elements of homological algebra.
• Homology theory of topological spaces.
• Homotopy groups.

Learning Outcomes

• Have a knowledge and understanding of topology demonstrated through the following topic areas:
• the fundamental group;
• the homology groups and their ranks;
• homotopy theory;
• homological algebra.

• Have developed advanced technical and scholastic skills in the areas of Topology and Algebra.

• Have highly specialised skills in the following area: Spatial awareness and Abstract reasoning.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve complex and specialised problems.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University