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 | CURVES AND SINGULARITIES | ||
| Code | MATH443 | ||
| 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 show how singularity theory can be applied to a variety of geometrical problems, including problems arising in applications such as the study of families of curves in the plane, wavefronts. |
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Learning Outcomes |
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A confident use of the singularity theory of functions of one variable, including unfolding theory, in concrete applications. A knowledge of fundamental constructions such as that of an envelope of curves or surfaces, and the dual of a curve or surface. A grounding in the theory of differentiable manifolds and transversality as geometrical tools. A preparation for further study of singularity theory, including functions of several variables and mappings, and elements of symplectic geometry. |
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Syllabus |
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| 1 |
1 Curves, and functions on them. Classification of functions up to R-equivalence. Regular values of smooth maps, manifolds. Applications. Envelopes of curves and surfaces. Unfoldings of function singularities. Criteria for versal unfolding. Applications |
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: |
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Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
| MATH101; 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:MMAS Year:1 Programme:G101 Year:3,4 |
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 semester | 100 | Standard University Policy | Assessment 1 Notes (applying to all assessments) Final exam rubric: All questions carry equal weight. Full marks can be obtained by fully answering FOUR questions. Only the best FOUR solutions will be counted. | |
| CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |