Module Details |
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module. |
Title | MANIFOLDS, HOMOLOGY AND MORSE THEORY | ||
Code | MATH410 | ||
Coordinator |
Dr A Pratoussevitch Mathematical Sciences Anna.Pratoussevitch@liverpool.ac.uk |
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Year | CATS Level | Semester | CATS Value |
Session 2016-17 | Level 7 FHEQ | First Semester | 15 |
Aims |
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To give an introduction to the topology of manifolds, emphasising the role of homology as an invariant and the role of Morse theory as a visualising and calculational tool. |
Learning Outcomes |
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To be able to: • give examples of manifolds, particularly in low dimensions; • compute homology groups, Euler characteristics and degrees of maps in simple cases; • determine whether an explicitly given function is Morse and to identify its critical points and their indices; • use the Morse inequalities to estimate the ranks of homology groups; • use the Morse complex to compute Euler characteristics and, in simple cases, homology. |
Syllabus |
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1 |
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Recommended Texts |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. Explanation of Reading List: |
Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
MATH101; MATH244; MATH102; MATH103 |
Co-requisite modules: |
Modules for which this module is a pre-requisite: |
Programme(s) (including Year of Study) to which this module is available on a required basis: |
Programme(s) (including Year of Study) to which this module is available on an optional basis: |
Programme:G101 Year:3 Programme:G101 Year:4 Programme:MMAS Year:1 |
Assessment |
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EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Written Exam | 2.5 hours | First | 100 | Yes | Standard UoL penalty applies | Assessment 1 Notes (applying to all assessments) Final exam rubric: All questions carry equal weight. Full marks can be obtained by fully answering FIVE questions. Only the best FIVE solutions will be counted. |
CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |