MAU34303 Discrete geometry
| Module Code | MAU34303 |
|---|---|
| Module Title | Discrete geometry |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Marvin Anas Hahn |
| Module Prerequisites |
MAU11100 Linear algebra and
MAU11201 Single-variable calculus |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 1.
- Continuous assessment contributes 10% towards the overall mark.
- Any failed components are reassessed, if necessary, by an exam in the reassessment session.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Apply basic theorems to structures in polyhedral geometry.
- Compute examples of polytopes, cones and fans from discrete input data.
- Describe various types of subdivisions of polytopes.
- Relate regular subdivisions to the secondary fan and secondary polytope.
- Apply basic theorems about Ehrhart polynomials and discrete volumes.
Module Content
- Polytopes
- Cones
- Fans
- Regular subdivisions
- Mixed subdivisions
- Secondary fans
- Secondary polytopes
- Discrete volumes
- Ehrhart polynomials
Recommended Reading
- Ziegler, Günter M. Lectures on polytopes. Springer 2012.
- Gelfand, Israel M., Kapranov, Mikhail M., and Zelevinsky, Andrei V.. Discriminants, resultants and multidimensional determinants. Springer 2008.